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(eiθ) and then get: f(eiθ) = eiθ/(1-eiθ) 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?