\begin{definition}[Definition:Sine/Complex Function]
The complex function $\sin: \C \to \C$ is defined as:
{{begin-eqn}}
{{eqn | l = \sin z
      | r = \sum_{n \mathop = 0}^\infty \paren {-1}^n \frac {z^{2 n + 1 } } {\paren {2 n + 1}!}
      | c = 
}}
{{eqn | r = z - \frac {z^3} {3!} + \frac {z^5} {5!} - \frac {z^7} {7!} + \cdots + \paren {-1}^n \frac {z^{2 n + 1 } } {\paren {2 n + 1}!} + \cdots
      | c = 
}}
{{end-eqn}}
\end{definition}