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.
Now, since and for all in the domain, it follows that maps fromt he unit disk into the upper half-plane.
Is this a sufficient answer to the question?
Thanks for the help