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Mobius Transformation

  1. Jan 31, 2009 #1
    I'm pretty stuck on this. I need to find a Mobius Transformation f such that

    [itex]f: \{ z: Im{z}>2 \} \rightarrow \{ w:|w-2|<3 \}[/itex]

    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. jcsd
  3. Jan 31, 2009 #2
    Do your notes say that Mobius transformations are determined by 3 images and preserve orientation?
  4. Jan 31, 2009 #3
    yes. i think so. how does this help us though?
  5. Feb 3, 2009 #4
    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.
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