Let D denote the unit disc |z|<1. Let the point A be inside D. Find a Mobius transformation which maps D bijectively onto itself and the point A to 0.
I'm really not sure how to do this. Are you supposed to pick three points in D and map them to where you want them to go, eg. A -> 0, and put them into some formula? I know a Mobius transformation has the form
f(z) = (az+b)/(cz+d),
I just don't know how to find a,b,c,d.
Thank you! x