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I'm trying to solve a problem which asks me to find a conformal mapping from the intersection of $\{z\in \mathbb{C}: |z-i|< \sqrt2$ with $|z+i|>\sqrt2\}$ onto the open unit disk.

I'm really new to these and I'm a bit lost because this doesn't resemble the examples I've seen so far.

Obviously the disk and the other region intersect at $±1$, but I have no idea how to go about using this to find the result.

As I said, I haven't really done many examples of conformal maps so I'd really appreciate if you could help walk me through this example.


marked as duplicate by Martin R, Did, user91500, mrtaurho, Lee David Chung Lin Jan 3 at 17:06

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  • $\begingroup$ @MartinR sorry, I realised I'd made a mistake - the second inequality should actually have been $>\sqrt2$ instead of $<$, and I assumed that was such a fundamental difference it merited a new question. Thanks so much for answering it though - it definitely did help with my understanding regardless. $\endgroup$ – oxsam Jan 2 at 22:59
  • $\begingroup$ I'm really sorry - I'm new to the site and didn't realise that was the appropriate thing to do. It won't happen again! $\endgroup$ – oxsam Jan 2 at 23:02
  • $\begingroup$ @MartinR I've tried applying the same approach to the newer problem but I can't see how to do it - I can't seem to work out what sector the area would map to. Would you be able to help a little more? Again, I'm really sorry for deleting it like that! $\endgroup$ – oxsam Jan 2 at 23:34
  • $\begingroup$ You asked this question here here. $\endgroup$ – Namaste Jan 3 at 2:47