{"id":9331,"date":"2018-02-09T15:54:18","date_gmt":"2018-02-09T10:24:18","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=9331"},"modified":"2018-03-17T09:54:17","modified_gmt":"2018-03-17T04:24:17","slug":"complex-numbers-and-quadratic-equations-class-11-notes-mathematics","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/","title":{"rendered":"Complex Numbers And Quadratic Equations class 11 Notes Mathematics"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#CBSE_Guide_Complex_Numbers_And_Quadratic_Equations_class_11_Notes\" >CBSE Guide Complex Numbers And Quadratic Equations class 11 Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#Complex_Numbers_And_Quadratic_Equations_class_11_Notes_Mathematics\" >Complex Numbers And Quadratic Equations class 11 Notes Mathematics<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#Download_Revision_Notes_as_PDF\" >Download Revision Notes as PDF<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#The_Complex_Numbers_And_Quadratic_Equations_class_11_Notes\" >The Complex Numbers And Quadratic Equations class 11 Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#CBSE_Class-11_Revision_Notes_and_Key_Points\" >CBSE Class-11 Revision Notes and Key Points<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>CBSE Mathematics Chapter 5 Complex Numbers And Quadratic Equations class 11 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Complex Numbers And Quadratic Equations class 11 Notes Mathematics latest chapter wise notes for quick preparation of CBSE exams and school based annual examinations. Class 11 Mathematics notes on Chapter 5 Complex Numbers And Quadratic Equations class 11 Notes Mathematics are also available for download in CBSE Guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Guide_Complex_Numbers_And_Quadratic_Equations_class_11_Notes\"><\/span>CBSE Guide Complex Numbers And Quadratic Equations class 11 Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>CBSE guide notes are the comprehensive notes which covers the latest syllabus of CBSE and NCERT. It includes all the topics given in NCERT class 11 Mathematics text book. Users can download CBSE guide quick revision notes from myCBSEguide mobile app and my CBSE guide website.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Complex_Numbers_And_Quadratic_Equations_class_11_Notes_Mathematics\"><\/span>Complex Numbers And Quadratic Equations class 11 Notes Mathematics<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Download CBSE class 11th revision notes for Chapter 5 Complex Numbers And Quadratic Equations class 11 Notes Mathematics in PDF format for free. Download revision notes for Complex Numbers And Quadratic Equations class 11 Notes Mathematics and score high in exams. These are the Complex Numbers And Quadratic Equations class 11 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.<\/p>\n<h1 style=\"text-align: center\"><span class=\"ez-toc-section\" id=\"Download_Revision_Notes_as_PDF\"><\/span><a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-11-chemistry\/1356\/cbse-revision-notes\/7\/\">Download Revision Notes as PDF<\/a><span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p style=\"text-align: center\"><strong>CBSE Class 11 Mathematics<br \/>\nRevision Notes<br \/>\nChapter-5<br \/>\nCOMPLEX NUMBERS AND QUADRATIC EQUATIONS<\/strong><\/p>\n<ol>\n<li><strong>Algebra, Modulus and Conjugate of Complex Numbers <\/strong><\/li>\n<li><strong>Argand Plane and Polar Representation <\/strong><\/li>\n<li><strong>Quadratic Equations<\/strong><\/li>\n<\/ol>\n<ul>\n<li><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\Rightarrow\" \/><\/span><\/span>\u00a0 \u00a0 \u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{i^2} = - 1\" \/><\/span><\/span><\/li>\n<li><strong>Imaginary Number: <\/strong>Square root of a negative number is called an Imaginary number. For example, <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\sqrt { - 5} ,\\sqrt { - 16} ,\" \/><\/span><\/span>\u00a0etc. are imaginary numbers.<\/li>\n<li><strong>Integral power of Iota (<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?i\" \/><\/span><\/span>)<\/strong>\u00a0: <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{i^p}\\left( {p &amp;gt; 4} \\right) = {i^{4q + r}}\" \/><\/span><\/span>\u00a0= <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\left( {{i^4}} \\right)^q}.{i^r} = {i^r},\" \/><\/span><\/span>\u00a0where <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\sqrt { - 1} = i\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{i^4} = 1\" \/><\/span><\/span><\/li>\n<li><strong>Complex Number<\/strong>: A number of the form <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{a }+~\\text{ib},\" \/><\/span><\/span>\u00a0where a and b are real numbers, is called a complex number, a is called the real part and b is called the imaginary part of the complex number.\u00a0It is denoted by <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?z.\" \/><\/span><\/span><\/li>\n<li><strong>Real part of <\/strong><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?z=a+ib\" \/><\/span><\/span>\u00a0is <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a\" \/><\/span><\/span>\u00a0and is denoted by <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?Re(z) = a\" \/><\/span><\/span>.<\/li>\n<li><b>Imaginary part of <\/b><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?z=a+ib\" \/><\/span><\/span>\u00a0is <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?b\" \/><\/span><\/span>\u00a0and is written as\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?Im(z) = b\" \/><\/span><\/span>.<\/li>\n<li><strong>Equality of complex numbers<\/strong>: Two complex numbers <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{z_1} = a + ib\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{z_2} = c + id\" \/><\/span><\/span>\u00a0are said to be equal, if <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a=c\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?b=d\" \/><\/span><\/span>.<\/li>\n<li><strong>Conjugate of a complex number<\/strong>: Two complex numbers are said to be conjugate of each other, if their sum is real and their product is also real. Conjugate of a complex number <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?z=a+ib\" \/><\/span><\/span>\u00a0is <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\overline z = a - ib\" \/><\/span><\/span>\u00a0i.e., conjugate of a complex number is obtained by changing the sign of imaginary part of z.<\/li>\n<li><strong>Modulus of a complex number<\/strong>: Modulus of a complex number <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?z=x+iy\" \/><\/span><\/span>\u00a0is denoted by <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left| z \\right| = \\sqrt {{x^2} + {y^2}}\" \/><\/span><\/span>.<\/li>\n<li><strong>Argument of a complex number <\/strong><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?x+iy\" \/><\/span><\/span>\u00a0: Arg<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?(x+iy)=\" \/><\/span><\/span>\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{\\tan ^{ - 1}}{y \\over x}\" \/><\/span><\/span>.<\/li>\n<li><strong>Representation of complex number as ordered pair<\/strong>: Any complex number <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a+ib\" \/><\/span><\/span>\u00a0can be written in ordered pair as <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left( {a,b} \\right)\" \/><\/span><\/span>, where a is the real past and b is the imaginary part of a complex number.<\/li>\n<li><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{Let }{{\\text{z}}_{1}}\\text{ }=\\text{ a }+\\text{ ib and }{{\\text{z}}_{2}}\\text{ }=\\text{ c }+\\text{ id}.\\text{ Then}\" \/><\/span><\/span><\/li>\n<\/ul>\n<p>(i) <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\text{z}}_{1}}\\text{+ }{{\\text{z}}_{2}}\\text{= (a + c) + i (b + d)}\" \/><\/span><\/span><\/p>\n<p>(ii) <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{\\text{z}}_{1}}{{\\text{z}}_{2}}\\text{= (ac -bd) + i (ad +bc)}\" \/><\/span><\/span><\/p>\n<ul>\n<li>Division of a complex number: If <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{z_1} = a + ib\" \/><\/span><\/span>\u00a0and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{z_2} = c + id\" \/><\/span><\/span>, then,<\/li>\n<\/ul>\n<p><span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{{z_1}} \\over {{z_2}}} = {{a + ib} \\over {c + id}} = {{\\left( {a + ib} \\right)\\left( {c - id} \\right)} \\over {\\left( {c + id} \\right)\\left( {c - id} \\right)}}\" \/><\/span><\/span>= <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{ac + bd} \\over {{c^2} + {d^2}}} + i{{bc - ad} \\over {{c^2} + {d^2}}}\" \/><\/span><\/span><\/p>\n<ul>\n<li>\u00a0\u00a0For any non-zero complex number <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{z }=\\text{ a }+\\text{ ib }\\left( \\text{a }\\ne \\text{ }0,\\text{ b }\\ne \\text{ }0 \\right),\" \/><\/span><\/span>\u00a0there exists the complex number\u00a0 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{a}{{{a}^{2}}+{{b}^{2}}}+i\\frac{-b}{{{a}^{2}}+{{b}^{2}}}\" \/><\/span><\/span>denoted by <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\frac{1}{z}\" \/><\/span><\/span>or\u00a0 <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{z}^{-1}}\" \/><\/span><\/span>, called the multiplicative inverse of z such that <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{(a + ib) }\\left( \\frac{{{a}^{2}}}{{{a}^{2}}+{{b}^{2}}}+i\\frac{-b}{{{a}^{2}}+{{b}^{2}}} \\right)\\text{=1+io=1}\" \/><\/span><\/span><\/li>\n<\/ul>\n<ul>\n<li><strong>Polar form of a complex number<\/strong>: The polar form of the complex number <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\text{z }=\\text{ x }+\\text{ iy is r }\\left( \\text{cos}\\theta \\text{ }+\\text{ i sin}\\theta\u00a0 \\right)\" \/><\/span><\/span>, where <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?r=\\sqrt{{{x}^{2}}+{{y}^{2}}}\" \/><\/span><\/span>\u00a0(the modulus of z) and <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?~\\text{cos}\\theta ~=\\frac{x}{r},\" \/><\/span><\/span>\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?~\\sin \\theta ~=\\frac{y}{r},\" \/><\/span><\/span>. (\u03b8 is known as the argument of z. The value of \u03b8, such that is called the principal argument of\u00a0 z.<\/li>\n<li><strong>Important properties<\/strong>:\u00a0\u00a0\u00a0\u00a0\u00a0 (i) <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left| {{z_1}} \\right| + \\left| {{z_2}} \\right| \\ge \\left| {{z_1} + {z_2}} \\right|\" \/><\/span><\/span>,\u00a0\u00a0\u00a0\u00a0\u00a0 (ii) <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?\\left| {{z_1}} \\right| - \\left| {{z_2}} \\right| \\le \\left| {{z_1} + {z_2}} \\right|\" \/><\/span><\/span><\/li>\n<li><strong>Fundamental Theorem of algebra<\/strong>: A polynomial equation of n degree has n roots.<\/li>\n<\/ul>\n<p><strong>Quadratic Equation<\/strong>:<\/p>\n<ul>\n<li><strong>Quadratic Equation<\/strong>: Any equation containing a variable of highest degree 2 is known as quadratic equation. e.g., <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a{x^2} + bx + c = 0\" \/><\/span><\/span>.<\/li>\n<li><strong>Roots of an equation<\/strong>: The values of variable satisfying a given equation are called its roots. Thus, <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?x = \\alpha\" \/><\/span><\/span>\u00a0is a root of the equation <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?p\\left( x \\right) = 0\" \/><\/span><\/span>\u00a0if <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?p\\left( \\alpha \\right) = 0.\" \/><\/span><\/span><\/li>\n<li><strong>Solution of quadratic equation<\/strong>: The solutions of the quadratic equation <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a{x^2} + bx + c = 0\" \/><\/span><\/span>, where <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a,b,c \\in {\\rm{R,}}\" \/><\/span><\/span>\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?a \\ne 0,\" \/><\/span><\/span>\u00a0\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{b^2} - 4ac &amp;lt; 0,\" \/><\/span><\/span>\u00a0 are given by <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?x = {{ - b \\pm i\\sqrt {4ac - {b^2}} } \\over {2a}}.\" \/><\/span><\/span><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"The_Complex_Numbers_And_Quadratic_Equations_class_11_Notes\"><\/span>The Complex Numbers And Quadratic Equations class 11 Notes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>CBSE Revision notes (PDF Download) Free<\/li>\n<li>CBSE Revision notes for Class 11 Mathematics PDF<\/li>\n<li>CBSE Revision notes Class 11 Mathematics \u2013 CBSE<\/li>\n<li>CBSE Revisions notes and Key Points Class 11 Mathematics<\/li>\n<li>Summary of the NCERT books all chapters in Mathematics class 11<\/li>\n<li>Short notes for CBSE class 11th Mathematics<\/li>\n<li>Key notes and chapter summary of Mathematics class 11<\/li>\n<li>Quick revision notes for CBSE exams<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_Class-11_Revision_Notes_and_Key_Points\"><\/span><strong>CBSE Class-11 Revision Notes and Key Points<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Complex Numbers And Quadratic Equations class 11 Notes Mathematics. CBSE quick revision note for class-11 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.<\/p>\n<ul>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-physics\/1340\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Physics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-chemistry\/1356\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Chemistry<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-mathematics\/1371\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-biology\/1388\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Biology<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-accountancy\/1411\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Accountancy<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-economics\/1423\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Economics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-business-studies\/1740\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Business Studies<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-computer-science\/1852\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Computer Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-informatics-practices\/1874\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Informatics Practices<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-11-geography\/1864\/cbse-revision-notes\/7\/\">Revision Notes for class-11 Geography<\/a><\/li>\n<\/ul>\n<p>To download Complex Numbers And Quadratic Equations class 11 Notes, sample paper for class 11 Chemistry, Physics, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n<ul>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/sets-class-11-notes-mathematics\/\">Sets class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/relations-functions-class-11-notes-mathematics\/\">Relations And Functions class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/trigonometric-functions-class-11-notes-mathematics\/\">Trigonometric Functions class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/principles-mathematical-induction-class-11-notes-mathematics\/\">Principles Of Mathematical Induction class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/\">Complex Numbers And Quadratic Equations class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/linear-inequalities-class-11-notes-mathematics\/\">Linear Inequalities class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/permutations-combinations-class-11-notes-mathematics\/\">Permutations And Combinations class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/binomial-theorem-class-11-notes-mathematics\/\">Binomial Theorem class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/sequences-and-series-class-11-notes-mathematics\/\">Sequences And Series class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/straight-lines-class-11-notes-mathematics\/\">Straight Lines class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/conic-sections-class-11-notes-mathematics\/\">Conic Sections class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/limits-and-derivatives-class-11-notes-mathematics\/\">Limits And Derivatives class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/mathematical-reasoning-class-11-notes-mathematics\/\">Mathematical Reasoning class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/statistics-class-11-notes-mathematics\/\">Statistics class 11 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/probability-class-11-notes-mathematics\/\">Probability class 11 Notes Mathematics<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>CBSE Mathematics Chapter 5 Complex Numbers And Quadratic Equations class 11 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Complex Numbers And Quadratic Equations class 11 Notes Mathematics latest chapter wise notes for quick preparation of CBSE exams and school based annual &#8230; <a title=\"Complex Numbers And Quadratic Equations class 11 Notes Mathematics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/\" aria-label=\"More on Complex Numbers And Quadratic Equations class 11 Notes Mathematics\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":9298,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,456],"tags":[457,150,567,461,426,240],"class_list":["post-9331","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-11","category-revision-notes","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-complex-numbers-and-quadratic-equations","tag-mathematics-notes","tag-quick-revision","tag-quick-revision-notes"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Complex Numbers And Quadratic Equations class 11 Notes Mathematics | myCBSEguide<\/title>\n<meta name=\"description\" content=\"Complex Numbers And Quadratic Equations class 11 Notes Mathematics Chapter 5 in PDF format for free download. Latest notes for CBSE exams.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Complex Numbers And Quadratic Equations class 11 Notes Mathematics | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Complex Numbers And Quadratic Equations class 11 Notes Mathematics Chapter 5 in PDF format for free download. Latest notes for CBSE exams.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/\" \/>\n<meta property=\"og:site_name\" content=\"myCBSEguide\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/mycbseguide\/\" \/>\n<meta property=\"article:published_time\" content=\"2018-02-09T10:24:18+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2018-03-17T04:24:17+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2018\/02\/11_maths_revision_notes.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"600\" \/>\n\t<meta property=\"og:image:height\" content=\"300\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"myCBSEguide\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@mycbseguide\" \/>\n<meta name=\"twitter:site\" content=\"@mycbseguide\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"myCBSEguide\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/\"},\"author\":{\"name\":\"myCBSEguide\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/f67796d5f5c5a468e8c680aaaad21519\"},\"headline\":\"Complex Numbers And Quadratic Equations class 11 Notes Mathematics\",\"datePublished\":\"2018-02-09T10:24:18+00:00\",\"dateModified\":\"2018-03-17T04:24:17+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/\"},\"wordCount\":967,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#organization\"},\"image\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2018\/02\/11_maths_revision_notes.jpg\",\"keywords\":[\"CBSE Notes\",\"CBSE Notes and Key Points\",\"Complex Numbers And Quadratic Equations\",\"Mathematics Notes\",\"Quick Revision\",\"Quick Revision Notes\"],\"articleSection\":[\"Class 11\",\"Revision Notes\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/\",\"url\":\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/\",\"name\":\"Complex Numbers And Quadratic Equations class 11 Notes Mathematics | myCBSEguide\",\"isPartOf\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2018\/02\/11_maths_revision_notes.jpg\",\"datePublished\":\"2018-02-09T10:24:18+00:00\",\"dateModified\":\"2018-03-17T04:24:17+00:00\",\"description\":\"Complex Numbers And Quadratic Equations class 11 Notes Mathematics Chapter 5 in PDF format for free download. Latest notes for CBSE exams.\",\"breadcrumb\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#primaryimage\",\"url\":\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2018\/02\/11_maths_revision_notes.jpg\",\"contentUrl\":\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2018\/02\/11_maths_revision_notes.jpg\",\"width\":600,\"height\":300,\"caption\":\"Notes for Sets\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mycbseguide.com\/blog\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"CBSE\",\"item\":\"https:\/\/mycbseguide.com\/blog\/category\/cbse\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Class 11\",\"item\":\"https:\/\/mycbseguide.com\/blog\/category\/cbse\/cbse-class-11\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Complex Numbers And Quadratic Equations class 11 Notes Mathematics\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#website\",\"url\":\"https:\/\/mycbseguide.com\/blog\/\",\"name\":\"myCBSEguide\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mycbseguide.com\/blog\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#organization\",\"name\":\"myCBSEguide\",\"url\":\"https:\/\/mycbseguide.com\/blog\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png\",\"contentUrl\":\"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png\",\"width\":180,\"height\":180,\"caption\":\"myCBSEguide\"},\"image\":{\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/mycbseguide\/\",\"https:\/\/x.com\/mycbseguide\",\"https:\/\/www.linkedin.com\/company\/mycbseguide\/\",\"http:\/\/in.pinterest.com\/mycbseguide\/\",\"https:\/\/www.youtube.com\/channel\/UCxuqSnnygFzwJG0pwogCNEQ\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/f67796d5f5c5a468e8c680aaaad21519\",\"name\":\"myCBSEguide\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Complex Numbers And Quadratic Equations class 11 Notes Mathematics | myCBSEguide","description":"Complex Numbers And Quadratic Equations class 11 Notes Mathematics Chapter 5 in PDF format for free download. Latest notes for CBSE exams.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/","og_locale":"en_US","og_type":"article","og_title":"Complex Numbers And Quadratic Equations class 11 Notes Mathematics | myCBSEguide","og_description":"Complex Numbers And Quadratic Equations class 11 Notes Mathematics Chapter 5 in PDF format for free download. Latest notes for CBSE exams.","og_url":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/","og_site_name":"myCBSEguide","article_publisher":"https:\/\/www.facebook.com\/mycbseguide\/","article_published_time":"2018-02-09T10:24:18+00:00","article_modified_time":"2018-03-17T04:24:17+00:00","og_image":[{"width":600,"height":300,"url":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2018\/02\/11_maths_revision_notes.jpg","type":"image\/jpeg"}],"author":"myCBSEguide","twitter_card":"summary_large_image","twitter_creator":"@mycbseguide","twitter_site":"@mycbseguide","twitter_misc":{"Written by":"myCBSEguide","Est. reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#article","isPartOf":{"@id":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/"},"author":{"name":"myCBSEguide","@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/f67796d5f5c5a468e8c680aaaad21519"},"headline":"Complex Numbers And Quadratic Equations class 11 Notes Mathematics","datePublished":"2018-02-09T10:24:18+00:00","dateModified":"2018-03-17T04:24:17+00:00","mainEntityOfPage":{"@id":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/"},"wordCount":967,"commentCount":0,"publisher":{"@id":"https:\/\/mycbseguide.com\/blog\/#organization"},"image":{"@id":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#primaryimage"},"thumbnailUrl":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2018\/02\/11_maths_revision_notes.jpg","keywords":["CBSE Notes","CBSE Notes and Key Points","Complex Numbers And Quadratic Equations","Mathematics Notes","Quick Revision","Quick Revision Notes"],"articleSection":["Class 11","Revision Notes"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/","url":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/","name":"Complex Numbers And Quadratic Equations class 11 Notes Mathematics | myCBSEguide","isPartOf":{"@id":"https:\/\/mycbseguide.com\/blog\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#primaryimage"},"image":{"@id":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#primaryimage"},"thumbnailUrl":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2018\/02\/11_maths_revision_notes.jpg","datePublished":"2018-02-09T10:24:18+00:00","dateModified":"2018-03-17T04:24:17+00:00","description":"Complex Numbers And Quadratic Equations class 11 Notes Mathematics Chapter 5 in PDF format for free download. Latest notes for CBSE exams.","breadcrumb":{"@id":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#primaryimage","url":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2018\/02\/11_maths_revision_notes.jpg","contentUrl":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2018\/02\/11_maths_revision_notes.jpg","width":600,"height":300,"caption":"Notes for Sets"},{"@type":"BreadcrumbList","@id":"https:\/\/mycbseguide.com\/blog\/complex-numbers-and-quadratic-equations-class-11-notes-mathematics\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mycbseguide.com\/blog\/"},{"@type":"ListItem","position":2,"name":"CBSE","item":"https:\/\/mycbseguide.com\/blog\/category\/cbse\/"},{"@type":"ListItem","position":3,"name":"Class 11","item":"https:\/\/mycbseguide.com\/blog\/category\/cbse\/cbse-class-11\/"},{"@type":"ListItem","position":4,"name":"Complex Numbers And Quadratic Equations class 11 Notes Mathematics"}]},{"@type":"WebSite","@id":"https:\/\/mycbseguide.com\/blog\/#website","url":"https:\/\/mycbseguide.com\/blog\/","name":"myCBSEguide","description":"","publisher":{"@id":"https:\/\/mycbseguide.com\/blog\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mycbseguide.com\/blog\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mycbseguide.com\/blog\/#organization","name":"myCBSEguide","url":"https:\/\/mycbseguide.com\/blog\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/","url":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png","contentUrl":"https:\/\/mycbseguide.com\/blog\/wp-content\/uploads\/2016\/04\/books_square.png","width":180,"height":180,"caption":"myCBSEguide"},"image":{"@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/mycbseguide\/","https:\/\/x.com\/mycbseguide","https:\/\/www.linkedin.com\/company\/mycbseguide\/","http:\/\/in.pinterest.com\/mycbseguide\/","https:\/\/www.youtube.com\/channel\/UCxuqSnnygFzwJG0pwogCNEQ"]},{"@type":"Person","@id":"https:\/\/mycbseguide.com\/blog\/#\/schema\/person\/f67796d5f5c5a468e8c680aaaad21519","name":"myCBSEguide"}]}},"_links":{"self":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts\/9331","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/comments?post=9331"}],"version-history":[{"count":4,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts\/9331\/revisions"}],"predecessor-version":[{"id":11702,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/posts\/9331\/revisions\/11702"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/media\/9298"}],"wp:attachment":[{"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/media?parent=9331"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/categories?post=9331"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mycbseguide.com\/blog\/wp-json\/wp\/v2\/tags?post=9331"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}