Q: Let . Show that maps the open unit disk into the upper half-plane , and maps the unit circle to the real line.

Im am not sure how to approach this. I found a problem similar to this one in my text book. Here is what I have worked out so far:

Since and for all , maps from the open disk of raduis 1 into the upper half plane.

I am not sure if I interpreting what I read correctly, so any help would be appreciated. Thanks.