\sin  z=\sum _{n=0}^{\infty } \frac{(-1)^nz^{2n+1}}{(2n+1)!}=z-\frac{z^3}{3!}+\frac{z^5}{5!}-\frac{z^7}{7!}+\frac{z^9}{9!}+\text{...} ,\forall z\in \mathbb{C}