  We study nilpotent Lie algebras endowed with a complex structure and a
quadratic structure which is pseudo-Hermitian for the given complex structure.
We propose several methods to construct such Lie algebras and describe a method
of double extension by planes to get an inductive description of all of them.
As an application, we give a complete classification of nilpotent quadratic Lie
algebras where the metric is Lorentz-Hermitian and we fully classify all
nilpotent pseudo-Hermitian quadratic Lie algebras up to dimension 8 and their
inequivalent pseudo-Hermitian metrics.
