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(Solved): 3. Prove that if a Mobius transformation f has exactly one fixed point in the extended complex pla ...
3. Prove that if a Mobius transformation has exactly one fixed point in the extended complex plane , then it is conjugate to the translation . That is, show that there exists a Mobius transformation such that .
Expert Answer
Solution : f is a mobius transformation so, ? a,b,c,d s.t.f(z)=az+bcz+dnow , it has only ine fix point, as given say z1.Hence, f(z1)=z1………..(1)n