Problem 1: 1.1. [6p] Let u(x, y) = 2y - 4x + axyb. a). Find the real values a and b for which u(x, y) is a harmonic function. b). Find the harmonic conjugate function v(x,y) of the harmonic function u(x, y) found in part a). c). Find the expression of an analytic function f(z) = u(x, y) + iv(x, y) expressed in terms of the complex variable z = x + iy, with u(x, y), v(x, y) found in parts a) and b). 1.2. [4p] Use Residue Theorem to evaluate the following integral: 5z+7 dz z + 2z-3 on C:|z2|= 6 in the counterclockwise direction.