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

Suppose that f(z) is analytic inside and on the simple closed contour C. If f(z) is 1-1 on Z, show that f(z) is 1-1 inside C.

2. Relevant equations

f(z) is 1-1 if f(z_{1})=f(z_{2}) implies z_{1}=z_{2}

f(z) is analytic at z_{0}if it equals some power series ∑c_{n}(z-z_{0})^{n}in some disk centered at z_{0}

3. The attempt at a solution

Not sure how to go about this. I get the feeling that there's some other important fact I should've included in the "relevant equations" field.

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# Suppose that f(z) is analytic inside and on the

Can you offer guidance or do you also need help?

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