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

Complex Wiener-It\^o Chaos Decomposition Revisited