Use conformal maps or combinations of conformal maps such as linear fractional transformations, powers, roots, sin z, log z, etc., to find a one-to-one analytic function mapping the given region D onto the upper half-plane U.

(1)

(2)

(3)

(4)

I'll try to do (1)

Answer:

If anyone could tell me if I'm on the right track and provide me with some help on the other problems, I would really appreciate it, thanks!