\cos  z=\sum _{n=0}^{\infty } \frac{(-1)^nz^{2n}}{(2n)!}=1-\frac{z^2}{2!}+\frac{z^4}{4!}-\frac{z^6}{6!}+\frac{z^8}{8!}-\frac{z^{10}}{10!}+\text{...} ,\forall z\in \mathbb{C}