Just wanted to point out an earlier thread on the topic at http://imechanica.org/node/1619

A message from Meghan Purdy:

Hi Professor Suo,

I just found this very useful website.  It lets you apply any Mobius transform to a lot of shapes on the z-plane, and it's really useful for checking answers on this homework.  You may want to pass this on to the other students.

http://www.math.ucla.edu/~tao/java/Mobius.html

Best,
Meghan Purdy