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.