Question: 2. Let C be the unit circle |z| = 1 in the complex plane, zo a general complex number, and define f (2) = and

2. Let C be the unit circle |z| = 1 in

2. Let C be the unit circle |z| = 1 in the complex plane, zo a general complex number, and define f (2) = and g(z) = ze'. These functions are used in all the parts below. (a) Prove that g is analytic everywhere in C. 2 (b) Explain why o g(z) dz = 0, and compute (explaining carefully, of course) o f(z) dz. 3 (c) If |zol

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