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.