TITLE: Find a conformal mapping which....
QUESTION [0 upvotes]: Find a conformal mapping which reflects the $|z|=1$ and $|z+2|=1$ circles in concentric circles with a center at the $z=2$ point.

REPLY [1 votes]: That is clearly impossible. The point $z=-1$ belongs to both circles, so assuming $\varphi$ is the wanted conformal mapping, $\varphi(-1)$ must simultaneously belong to two concentric circles.
{"set_name": "stack_exchange", "score": 0, "question_id": 1422174}