We introduce and study variational inequalities in the complex domain, along with some technical tools useful in their study. We then extend to the complex domain some recent developments in the field of the distributed solution of (generalized) Nash equilibrium problems. In order to illustrate our techniques we consider some new MIMO games over vector Gaussian Interference Channels, modeling some distributed resource allocation problems in MIMO cognitive radio systems and femtocells. These games are examples of Nash equilibrium problems that can not be handled by current methodologies.