  In this article, some properties of complex Wiener-It\^o multiple integrals
and complex Ornstein-Uhlenbeck operators and semigroups are obtained. Those
include Stroock's formula, Hu-Meyer formula, Clark-Ocone formula and the
hypercontractivity of complex Ornstein-Uhlenbeck semigroups. As an application,
several expansions of the fourth moments of complex Wiener-It\^o multiple
integrals are given.
