Let $r_0, r_1, \ldots, r_N \in \mathbb{C}$ each be a D1207: Complex number.
The complex polynomial function with respect to $r_0, r_1, \ldots, r_N$ is the D4881: Complex function \begin{equation} \mathbb{C} \to \mathbb{C}, \quad z \mapsto \sum_{n = 0}^N r_n z^n \end{equation}