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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.

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

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ @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