Let $\mathbb{C}$ be the D372: Set of complex numbers.
The standard complex sine function is the D4881: Complex function \begin{equation} \sin : \mathbb{C} \to \mathbb{C}, \quad \sin(z) = \frac{z^1}{1 !} - \frac{z^3}{3 !} + \frac{z^5}{5 !} - \frac{z^7}{7 !} + \cdots \end{equation}