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Let \(z\) be a nonreal complex number such that \(|z| = 1.\) Find the real part of \(\frac{1}{1 - z}.\)

 Mar 4, 2021
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Awww please don't be sad. 

I was just doing some alcumus and by the time I got 5 questions wrong, I was about to cry. 

Considering I just failed by last 5 algebra problems, idk how much you should trust my answer, but I'll give it a try. 

 

z = a + bi

b = 0 since we're looking for the real part of z. 

z = a + 0i

a^2 +0i^2 = 1^2

a = +/- 1

Testing for both, a can't be 1, since 1/0 doesn't exist. 

Therefore, a = -1. 

1/(1--1) = 1/2

 

I hope this helps. :)))

 

=^._.^=

 Mar 5, 2021

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