- #1
Sammicalvin
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Homework Statement
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
Homework Equations
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