1. The problem statement, all variables and given/known data Let D be a simply connected region in C (complex domain) and let C be a simple closed curve contained in D. Let f(z) be analytic in D. Suppose that z0 is a point which is not enclosed by C. What is 1/(2πi)∫f(z)/(z-z0)dz? 2. Relevant equations Cauchy's formula: f(z0) = 1/(2πi)∫f(z)/(z-z0)dz 3. The attempt at a solution I have a gut feeling that since z0 is not in enclosed by C, it is also not part of D. Since f(z) is analytic in D, this somehow means that f(z) = 0 outside of D so f(z0) = 0. I know I'm missing a lot of connections and mathematical reasoning, but this is a guess I have because I don't actually know how to show it mathematically. Help appreciated!