Answer Happy

Please answer the following two questions fully please
Question 5 - 10 marks Let f(z) = (1 – 2) (22)” (=| < 1/2) na0 and 9(3) - Σ. (1) (Re: <0). ) n=0 [8] (a) Prove that f and g are direct analytic continuations of each other. (b) Find a complex number z with Rez > 0 for which the series n Σ(Ε) n=0 converges. [2] Question 6 10 marks Let f(x) = 22 + ze. (a) Prove that f is one-to-one near 0. (b) Invert the Taylor series about 0 for f, giving the first three non-vanishing terms. [2] [8] ]