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(z1)=f(z2) implies z1=z2 f(z) is analytic at z0 if it equals some power series ∑cn(z-z0)n in some disk centered at z0 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.