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# riemann sphere, mobius transformations watch

1. hello IA.

Let C1, C2 be two disjoint circles on the riemann sphere. show there is a mobius transformation that maps them to two circles in C (complex plane) centred on the origin.

bit confused. we can think of a mobius transformation as a rotation of the riemann sphere, right? for the circles to share the same centre then in C, they're both going to need to have their centres going through the north-south pole of the sphere, right? but there isn't necessarily a rotation that does this? confused.
2. Not all Mobius transformations are rotations (or am I missing something)
3. Ok, put another way, we want to map two points - the centres - to one point - 0. But mobius maps wont do this??
4. The centres don't always map to centres.
5. (Original post by Chewwy)
Ok, put another way, we want to map two points - the centres - to one point - 0. But mobius maps wont do this??
Map one centre to the south pole and another to the north pole.

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