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Complex Analysis : Mobius Transformation

1). Let D = {z: |z| < 1 } and find all Mobius transformations T such that T(D) = D.

2). 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).

Solution Summary

Mobius transformations are investigated. The solution is detailed and well presented.