A complex function that is harmonic but not analytic [closed]

Can someone give a simple example of a complex function that is harmonic but not analytic?

Thanks.

D.

• Natural examples are $\mbox{Re}\;z, \mbox{Im}\; z, \bar{z}$... – Julien Mar 2 '13 at 20:35

$x{}{}{}{}{}{}{}{}{}{}{}{}{}{}$
• You probably mean $z\mapsto\mathrm{Re}(z)$. – Philippe Malot Mar 2 '13 at 20:20