# Harmonic Functions (Complex Analysis)

• October 29th 2008, 08:17 PM
Decide whether each of the following functions $u$ is harmonic, if so, find a harmonic conjugate.
(1) $u(x,y) = x^4 -6x^2y^2 + y^4$
(2) $u(x,y) = \frac{x^2}{x^2 + y^2 + 1}$
OK It is harmonic if it satisfies $u_{xx}+x_{yy}=0$. Then find the corresponding v which satisfies the C-R equations.