Let a and b be two complex numbers with b 0. Consider the function f(z) za...

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Let a and b be two complex numbers with b 0. Consider the function f(z) za bz - 1 defined on the set D = C\ {}. Suppose 1, -1, ¡ E D and |f(1) = f(-1) | = |f(i) | = 1. (1) Show that ba and f(z) = 1 for all z ED with Iz | = 1. (ii) Show that f(z) is a constant function if la = 1. Let a and b be two complex numbers with b 0. Consider the function f(z) za bz - 1 defined on the set D = C\ {}. Suppose 1, -1, ¡ E D and |f(1) = f(-1) | = |f(i) | = 1. (1) Show that ba and f(z) = 1 for all z ED with Iz | = 1. (ii) Show that f(z) is a constant function if la = 1.

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i Suppose lzl1 Then we have 1fracfzf1 fraczalz1 cdot fraczbzbl fraczalz1 Plugging in z1 we get frac1... View the full answer