Definition:Cosine/Complex Function

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


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

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