Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

I need to find a mapping for $z + \frac{1}{z}$ to the $x$-axis. I have that $f(i) = 0$, $f(-1)= -2$ and $f(1) = 2$. I am not sure as to what my professor seems to be asking us to think of in this example he used. What is the function that maps the line $z + \frac{1}{z}$ to the $x$-axis?

share|cite|improve this question
How is $z+\frac{1}{z}$ a line? Is the question actually asking for the preimage of the real line under the map $z\mapsto z+1/z$? (This is just a guess.) – anon Apr 30 '12 at 8:37
Circles are lines in the complex extended plane. A half circle is a line in the upper half plane. – Low Scores Apr 30 '12 at 8:39
The preimage of the reals under this map is the real line (which is of course a circle on $\Bbb C^*$) in union with the unit circle. Is this relevant to your question? (To me, $z+\frac{1}{z}$ is a symbolic expression in the complex variable $z$. I don't know in what sense you understand it to be a line.) – anon Apr 30 '12 at 8:50

Your Answer


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

Browse other questions tagged or ask your own question.