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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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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