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Find sqaure root of 1+i

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Find sqaure root of 1+i

Posted by Simran Kaur 1 year, 6 months ago

CBSE > Class 11 > Mathematics

2 answers

Jiyaaaaaaaaaa Sood 1 year, 6 months ago

Let tye square root of 1+i =root over 1+i Root over 1+i=x+iy By Squaring both sides We get , 1+i=(x+iy)² 1+i=x²+y²i²+2xyi As we know that i²=-1 So,, 1+i=x²-y²+2xyi Now compare real part and imaginary part on both sides... 1=x²-y²----1 equation 1=2xy------2equatiin We know a identwe says that (x²+y²)²=(x²-y²)²+(2xy)² Now put the values in this identity On adding and subtracting the above equations , we get ∴x2=22+1 and y2=22−1. ∴x=±22+1andy=±22−1 So, by equation (1), 1−i=22+1−i22−1 Ans: 1

Aryan Choudhary 1 year, 6 months ago

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