- #1
mimsy57
- 18
- 0
I'm looking for the error in my understanding here, not help with the problem itself. I'm making some kind of mistake, so I've listed out everything I think I know, and I'm hoping someone can either tell me what I'm misunderstanding, or tell me there is an error in the problem statement:
Problem Statement: find the Mobius transformation taking the circle |z|=1 to |z+2|=1 such that T(-1)=-3 and T(i)=-1.
What I think:
*Both the circle and its image have radius 1, with the first centered at the origin and the second at -2.
*The additional points we are given mappings for are -1 and i, which are the endpoints to an arc of a quarter circle. These are mapping to -3 and -1 which are the bounds for the half circle. This implies the mapping is going around twice for once around the circle being mapped, which would imply it is not a bijection, and Mobius transformations are bijections.
Problem Statement: find the Mobius transformation taking the circle |z|=1 to |z+2|=1 such that T(-1)=-3 and T(i)=-1.
What I think:
*Both the circle and its image have radius 1, with the first centered at the origin and the second at -2.
*The additional points we are given mappings for are -1 and i, which are the endpoints to an arc of a quarter circle. These are mapping to -3 and -1 which are the bounds for the half circle. This implies the mapping is going around twice for once around the circle being mapped, which would imply it is not a bijection, and Mobius transformations are bijections.