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

Find real part of $\left(\frac{a+bi}{a-bi}\right)^2-\left(\frac{a-bi}{a+bi}\right)^2$, for any $a,b$ (they are real numbers)

Please help guys

share|cite|improve this question
$z+\overline z=2\operatorname{Re}z$. – Marc van Leeuwen Oct 12 '12 at 7:07
up vote 2 down vote accepted

HINT: Plug in some numbers, calculate $\overline{\left(\frac{a+bi}{a-bi}\right)^2}$ and think about Marc's comment.

share|cite|improve this answer

Let $A+iB=(a+ib)^2,$ so $A-iB=(a-ib)^2$





So the number is purely imaginary.

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.