  This paper deals with complex structures on Lie algebras $\ct_{\pi} \hh=\hh
\ltimes_{\pi} V$, where $\pi$ is either the adjoint or the coadjoint
representation. The main topic is the existence question of complex structures
on $\ct_{\pi} \hh$ for $\hh$ a three dimensional real Lie algebra. First it was
proposed the study of complex structures $J$ satisfying the constrain $J\hh=V$.
Whenever $\pi$ is the adjoint representation this kind of complex structures
are associated to non singular derivations of $\hh$. This fact derives
different kind of applications. Finally an approach to the pseudo K\"ahler
geometry was done.
