\begin{definition}[Definition:Polynomial/Complex Numbers]
A '''polynomial (in $\C$)''' is an expression of the form:
:$\ds \map P z = \sum_{j \mathop = 0}^n \paren {a_j z^j} = a_0 + a_1 z + a_2 z^2 + \cdots + a_{n - 1} z^{n - 1} + a_n z^n$
where:
:$z \in \C$
:$a_0, \ldots a_n \in \mathbb k$ where $\mathbb k$ is one of the standard number sets $\Z, \Q, \R, \C$.
\end{definition}