Taylor series of cosine

Theorem: Let $z_0 \in \mathbb{C}$. The following Taylor series holds: $$\cos(z)= \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k (z-z_0)^{2k}}{(2k)!},$$ where $\cos$ denotes the cosine function.

Proof: █