Question: Complex Analysis Let f : C C be a one-to-one and onto analytic function. Consider the function F(z) = f(1/z). (i) Show that z =

Complex Analysis

Let f : C C be a one-to-one and onto analytic function. Consider the function F(z) = f(1/z).

(i) Show that z = 0 cannot be an essential singularity of F.

(ii) Show that z = 0 cannot be a removable singularity of F.

(iii) What is the order of the pole of F at z = 0 and what can you conclude about f ?

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