# Homework Help: The complex function

1. Nov 19, 2009

### Void123

1. The problem statement, all variables and given/known data

How would I prove that $$ln (z)$$ is analytic?

2. Relevant equations

...

3. The attempt at a solution

I rewrote it as $$ln (z) = ln (r) + i\theta$$. But, I'm not quite sure how to apply Cauchy-Riemman conditions here.

2. Nov 19, 2009

### clamtrox

$$\frac{\partial f}{\partial x} = \frac{\partial f}{\partial r}\frac{\partial r}{\partial x} + \frac{\partial f}{\partial \theta}\frac{\partial \theta}{\partial x}$$

if you want to use the polar coordinates. Remember also that CR-equation can be written as

$$i \frac{\partial f}{\partial x} = \frac{\partial f}{\partial y}.$$