(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the function f(z) = z/(1-z) maps the unit circle to an infinite line.

2. Relevant equations

Polar form z = rexp(iθ)

3. The attempt at a solution

I've tried to see what happens, when we let f(z) = f(e^{iθ}) and then get:

f(e^{iθ}) = e^{iθ}/(1-e^{iθ})

But I need some help on making this expression more illuminating. I want something for which I can take the real and imaginary part - what tricks can I use?

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# Homework Help: Show that function maps unit cirle onto a line

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