(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Homework Help: Mobius Map

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