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.
So, just to be clear, the conjugate of is and the conjugate of is ? If so, this means I alwars change the sign and take the conjugate of the complex number in the expression. Correct?
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