Question

Upper half plane maps to upper half plane in mobius transformation

Answer 1

Finding a Mobius transformation that maps the upper half-plane {Im(z)>0};z∈C to the inside of a unit-disk, such that point i is mapped to 0 and ∞ to −1.

Okay, to be clear, I know that a Mobius transformation w is of the form:

w=az+bcz+d;ad−bc≠0.I am very aware of what a unit disk is. I have done assignments like finding an mobius transformation that maps some points (C) a,b,c to d,e,f. -Where these points were not infinity.