Question

Let a be inside set of complex no. such that modulus of a < 1. Define f(b) = (b-a)/(1-āb) for b inside set of complex no. \ { ā^-1}.

(a) Let modulus of b = 1. Prove that modulus of f(b) =1.

(b) Let modulus of b<1. Prove that modulus of f(b)<1.