Algebra and Geometry | Part IA, 2002

(a) Suppose that gg is a Möbius transformation, acting on the extended complex plane. What are the possible numbers of fixed points that gg can have? Justify your answer.

(b) Show that the operation cc of complex conjugation, defined by c(z)=zˉc(z)=\bar{z}, is not a Möbius transformation.

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