# Definition:Polynomial/Complex Numbers

## Definition

A polynomial (in $\C$) is an expression of the form:

$\displaystyle P \left({z}\right) = \sum_{j \mathop = 0}^n \left({a_j z^j}\right) = a_0 + a_1 z + a_2 z^2 + \cdots + a_{n-1} z^{n-1} + a_n z^n$

where:

$z \in \C$
$a_0, \ldots a_n \in \mathbb k$ where $\mathbb k$ is one of the standard number sets $\Z, \Q, \R, \C$.