# Mobius Transformation

1. Jan 31, 2009

### latentcorpse

I'm pretty stuck on this. I need to find a Mobius Transformation f such that

$f: \{ z: Im{z}>2 \} \rightarrow \{ w:|w-2|<3 \}$

I don't really have any ideas here. My notes aren't really helping here either. Can anybody point me in the right direction?

2. Jan 31, 2009

### mutton

Do your notes say that Mobius transformations are determined by 3 images and preserve orientation?

3. Jan 31, 2009

### latentcorpse

yes. i think so. how does this help us though?

4. Feb 3, 2009

### mutton

I think this will work: Pick 3 points on the line Im z = 2 that go in a certain direction. Say you pick them such that the half plane is on their right. For their images under the Mobius transformation, pick 3 points on the circle |w - 2| = 3 such that the interior of the circle is also on their right.