I understand using Laplace transforms but I think this is something different the question reads.

Show that the following functions $\displaystyle u(x,y)$ are harmonic (ie satisfy Laplace's equation) and in each case find $\displaystyle f(z)$ such that $\displaystyle f(z) = u + iv$ is regular.

(a) $\displaystyle u = x^4 - 6x^2y^2 + y^4$Any help would be great.

(b)$\displaystyle u = sinxsinhy$

Jez