Question 1:

(a) Formulate uniqueness theorem for holomorphic functions. (b) Let C be the curve y = 23+ 2x2 - 2., joining points (0, 0) and (1, 1). Evaluate / (42 2 - 2 1 z) dz. C(a) Formulate Residue theorem for a function holomorphic in a punctured region (Without nitely many singular points). (b) Use Cauchy's Integral Theorem or Formula to evaluate / 22 Z3 3122+4z 121 |z|=1 Hint: One of the roots of the equation 233122+4z 121: 0 is z : 3 1. Find two other roots before applying Cauchy's theorem