Q6. Work out the following: (a) Apply the Cauchy-Goursat Theorem to infer that c f (z) = 0 where i. Sc Log(z+ 2) dz where C = {z: z = 1} ii. Scdz where C = {z: |z| = 1} (b) Let P(z) = a + az + a2z + + anz" where an 0 and ao, a, constants. Then verify that ., an are complex i. 1 z P'(z) P(z) dz = - an-1 an zp'(z) ii. dz = 2 P(z) 2anan-2-an-12 2 an (c) Prove the Liouville's Theorem.