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The complex Wishart distribution has ample applications in science and engineering. In this paper, we give explicit expressions for E (tr (W h)) g (tr (W j)) i and E (tr (W − h)) g (tr (W − j)) i , respectively, for particular values of g, h, i, j, g + h + i + j ≤ 5 , where W follows a complex Wishart distribution. For specific values of g, h, i, j, we first write (tr (W h)) g (tr (W j)) i and (tr (W − h)) g (tr (W − j)) i in terms of zonal polynomials and then by using results on integration evaluate resulting expressions. Several expected values of matrix-valued functions of a complex Wishart matrix have also been derived. [ABSTRACT FROM AUTHOR]