Mobius Transformation for Im(z) > 2 to |w-2| < 3

[latentcorpse]

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

f: \{ z: Im{z}&gt;2 \} \rightarrow \{ w:|w-2|&lt;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?

 

[mutton]

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

 

[latentcorpse]

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

 

[mutton]

I think this will work: Pick 3 points on the line I am 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.