# Maximum Modulus Principle question

1. Sep 12, 2011

### bachdylan

Last edited by a moderator: May 5, 2017
2. Sep 12, 2011

### micromass

OK, I was hoping that other people might reply, because my solution is fishy. But let's do this anyway.

Basically, what you need to do is showing that the function extends to $\infty$. So infinity is a singularity, and we want to extend our function to this singularity.

Now, because infinity is tough to work with, we are going to replace our singularity. So show that our problem is equivalent to a problem where the function is undefined in 0 (for example).

Try to show this by using either the Riemann mapping theorem or by working with the transformation $z\rightarrow \frac{1}{z}$.

Are you following me?