Let $\mathbb{C}$ be the D372: Set of complex numbers.
The set of euclidean complex numbers with respect to $N \in 1, 2, 3, \ldots$ is the D11: Set $$\begin{equation} \mathbb{C}^N = \prod_{n = 1}^N \mathbb{C} = \{ z \mid z : \{ 1, \ldots, N \} \to \mathbb{C} \} \end{equation}$$