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Mobius Transformations

Prove that if T is a Mobius transformation such that T(0) = 0, then T may be written as T(z) = z/(cz+d) for some choices of c and d.

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General Mobius transformation is T = (az+b)/(cz+d), where

ad-bc not= 0 ...

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A Mobius transformation is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.