\[ \begin{align} \operatorname{sen}iz &=\frac{\operatorname{e}^{i.iz}-\operatorname{e}^{-i.iz}}{2i}=\frac{\operatorname{e}^{i^{2}z}-\operatorname{e}^{-i^{2}z}}{2i}=\frac{\operatorname{e}^{-z}-\operatorname{e}^{-(-z)}}{2i}.\frac{i}{i}\text{=}\\ &=i\frac{\operatorname{e}^{-z}-\operatorname{e}^{z}}{2i^{2}}=-i\frac{\operatorname{e}^{z}-\operatorname{e}^{-z}}{-2}=i\frac{\operatorname{e}^{z}-\operatorname{e}^{-z}}{2} \end{align} \]