Assignment:
Q1). Let D = {z: |z| < 1 } and find all Mobius transformations T such that T(D) = D.
Q2). Show that a Mobius transformation T satisfies T(0) = infinity and T ( infinity) = 0 if and only if Tz = az^-1 for some a in C ( C is complex plane).
Provide complete and step by step solution for the question and show calculations and use formulas.