# Complex Analysis

1. Apr 16, 2009

### oab729

1. The problem statement, all variables and given/known data
Prove that there does not exist an analytic function on the annulus D: 1<|z|<2, s.t. F'(z) = 1/z for all z in D.

2. Relevant equations

3. The attempt at a solution
Assume F exists, then for z in D, not a negative number, F(z) = Log z + c since Log' z = 1/z... Lost

2. Apr 17, 2009

### Billy Bob

Find a path C such that $$\int_C \frac1z\,dz\neq0$$