- #1

bbdynamite

- 3

- 0

## Homework Statement

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 z

_{0}is a point which is not enclosed by C. What is 1/(2πi)∫f(z)/(z-z

_{0})dz?

## Homework Equations

Cauchy's formula: f(z

_{0}) = 1/(2πi)∫f(z)/(z-z

_{0})dz

## The Attempt at a Solution

I have a gut feeling that since z

_{0}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(z

_{0}) = 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!