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Homework Help: Mobius Map

  1. Feb 9, 2010 #1
    1. The problem statement, all variables and given/known data
    Suppose T is a Mobius map take Real -> Real and infinite infinitely to 0
    a) What's the image of the family of lines parallel to Real?
    b) What's the image of the family of lines perpendicular to Real?
    c) Show the Mobius map take D = {z :|z|<1} onto itself iff Tz = e^i(theta) * (z-a)/(1-az)
    for a belongs to D and theta belongs to Real
    d) C1 and C2 are disjoint circles in Complex . Show there's a Mobius map s.t. TC1 and TC2 are concentric

    2. Relevant equations



    3. The attempt at a solution
    a) Since the mobius map take infinitely to 0, we are expect to get a circle through 0?
    b) Since the mobius map take infinitely to 0, we are expect to get a circle through 0 and perpendicular to Real? (since mobius map preserves angle)?
    c) let z = e^iT ???
    d) i hv no idea
     
  2. jcsd
  3. Feb 12, 2010 #2
    Neat questions. I dont have a clue either.
    Anyone wanna help?
     
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