ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5128 on D164: Standard complex sine function
Standard complex sine function expressed in terms of complex exponential function
Formulation 0
Let $\sin$ be the D164: Standard complex sine function.
Let $z \in \mathbb{C}$ be a D1207: Complex number.
Then \begin{equation} \sin z = \frac{e^{i z} - e^{- i z}}{2 i} \end{equation}
Formulation 1
Let $\sin$ be the D164: Standard complex sine function.
Let $z \in \mathbb{C}$ be a D1207: Complex number.
Then \begin{equation} \sin z = \frac{\exp(i z) - \exp(- i z)}{2 i} \end{equation}