Decide whether each of the following functions $\displaystyle u$ is harmonic, if so, find a harmonic conjugate.

(1) $\displaystyle u(x,y) = x^4 -6x^2y^2 + y^4$

(2) $\displaystyle u(x,y) = \frac{x^2}{x^2 + y^2 + 1}$

Can someone walk me through one of these too, please? Thanks!