\begin{definition}[Definition:Cosine/Complex Function]
The complex function $\cos: \C \to \C$ is defined as:
{{begin-eqn}}
{{eqn | l = \cos z
      | r = \sum_{n \mathop = 0}^\infty \paren {-1}^n \frac {z^{2 n} } {\paren {2 n}!}
      | c = 
}}
{{eqn | r = 1 - \frac {z^2} {2!} + \frac {z^4} {4!} - \frac {z^6} {6!} + \cdots + \paren {-1}^n \frac {z^{2 n} } {\paren {2 n}!} + \cdots
      | c = 
}}
{{end-eqn}}
\end{definition}