Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How to show that $\Re(\frac{e^{i \theta}+z}{e^{i \theta}-z})=\frac{1+|z|^2}{|z-e^{i \theta}|^2}$?

I have got $\Re(\frac{e^{i \theta}+z}{e^{i \theta}-z})=\frac{1+|z|}{1-|z|}$. Is this right?

share|cite|improve this question
Does $|w+z|=|w|+|z|$ hold? Try $z = -w$. – Lord_Farin Apr 4 '13 at 8:51
Both statements are wrong. Try $\theta = 0$, $z = -1$ to see this. It should be $1-|z|^2$ in the numerator. Show us your work so that we can tell you what went wrong. – Ayman Hourieh Apr 4 '13 at 11:39
up vote 0 down vote accepted

Hint: $\Re z= \frac{1}{2}(z+z^*)$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.