Relativizations of the $P=NP$ problem over the complex number field

In this article we consider the relativised polynomial complexity classes $P_{\mathbb C}$ and $DNP_{\mathbb C}$ over the complex number field $\mathbb C$, defined in the frames of an approach to generalized computability, considered in [1]. We prove that $P_{\mathbb C}^{\mathbb Z}\ne DNP_{\mathbb C}^{\mathbb Z}$, where the oracle $\mathbb Z$ is the set of integers.