  Nodal domains are studied both for real $\psi_R$ and imaginary part $\psi_I$
of the wavefunctions of an open microwave cavity and found to show the same
behavior as wavefunctions in closed billiards. In addition we investigate the
variation of the number of nodal domains and the signed area correlation by
changing the global phase $\phi_g$ according to
$\psi_R+i\psi_I=e^{i\phi_g}(\psi_R'+i\psi_I')$. This variation can be
qualitatively, and the correlation quantitatively explained in terms of the
phase rigidity characterising the openness of the billiard.
