# Homework Help: Mobius Map

1. Feb 9, 2010

### Sammicalvin

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. Feb 12, 2010

### Socrates' Pen

Neat questions. I dont have a clue either.
Anyone wanna help?