1. Illustrate that function x^{2}+iy^{3} is not analytic anywhere. Reconcile with fact that cauchy-riemann equations are satisfied at x=0 , y=0.
2. Find which of the given functions u are harmonic. For every harmonic function, determine conjugate harmonic function v and express u + i v as analytic function of z.
i) 3x^{2}y+2x^{2}-y^{3}-2y^{2}
ii) 2xy+3xy^{2}-2y^{3}
iii) xe^{x} cosy-ye^{x}siny
iv) e^{-2xy}sin(x^{2}-y^{2})