Letz +iye C. 2.1 Let u(x,y)+xy+ay + by be a given real valued function. 2.1.1 Find the values of a and b for which u will be harmonic. (6) 2.1.2 Find the harmonic conjugate v of u for those values of a and b obtained in (2.1.1). (6) 2.1.3 Find the most general analytic function f(z) of the variable z = x + iy whose real part is u. Express your answer explicitly in z. (6) 2.2 Show that f(z) = 3+ is nowhere analytic by showing that wherever it satisfies the Cauchy-Riemann equations it is not holomorphic. (10)