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Sia ? 6 years, 3 months ago
sin(theta) = cos(90 - theta) and cos(theta) = sin(90 - theta)
Thus cos 90 = sin 0 = 0
cos (90) = 0
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Basic math glossary-W define words beginning with the letter W. w: w is an abbreviation for width. Weight: A measure of how heavy an object is . Whole numbers: Whole numbers include the natural numbers and 0, such as 0, 1, 2, 3, 4, 5, 6, ... Width:The distance across or the measure of how wide something is.
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Sia ? 6 years, 3 months ago
Let {tex}x + yi = \sqrt { - 15 - 8i} {/tex}
Squaring both sides, we get
(x + yi)2 = -15 - 8i
x2 - y2 + 2xyi = -15 - 8i
Comparing the real and imaginary parts
x2 - y2 = -15 .... (i)
{tex}2xy = - 8 \Rightarrow xy = - 4{/tex}
Now, we know that
(x2 + y2)2 = (x2 - y2) + 4x2y2
= (-15)2 + 4(-4)2
= 225 + 64
= 289
{tex}\therefore {x^2} + {y^2} = 17{/tex} ..... (ii) [Neglecting (-) sign as x2 + y2 > 0]
Solving (i) and (ii), we get
{tex}x = \pm 1{/tex} and {tex}y = \pm 4{/tex}
Since the sign of xy is (-)
{tex}\therefore{/tex} x = 1, y = -4
And x = -1, y = 4
{tex}\therefore \sqrt { - 15 - 8i} = \pm (1 - 4i){/tex}
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