Definition:Sine/Complex Function

Definition
The complex function $\sin: \C \to \C$ is defined as:


 * $\displaystyle \sin z = \sum_{n \mathop = 0}^\infty \left({-1}\right)^n \frac {z^{2n+1}}{\left({2n+1}\right)!}$

It follows from Power Series over Factorial that these power series converge for all values of $z \in \C$.