\[ \begin{align} \operatorname{sen}i&=\frac{\operatorname{e}^{i.i}-\operatorname{e}^{-i.i}}{2i}=\frac{\operatorname{e}^{i^{2}}-\operatorname{e}^{-i^{2}}}{2i}=\frac{\operatorname{e}^{-1}-\operatorname{e}^{-(-1)}}{2i}.\frac{i}{i}\text{=}\\ &=i\frac{\operatorname{e}^{-1}-\operatorname{e}^{1}}{2i^{2}}=-i\frac{\operatorname{e}^{1}-\operatorname{e}^{-1}}{-2}=i\frac{\operatorname{e}^{1}-\operatorname{e}^{-1}}{2} \end{align} \]