ThmDex – An index of mathematical definitions, results, and conjectures.

ThmDex – An index of mathematical definitions, results, and conjectures.

Result R5129 on D165: Standard complex cosine function

Standard complex cosine function expressed in terms of complex exponential function

Formulation 0

Let $\cos$ be the D165: Standard complex cosine function.
Let $z \in \mathbb{C}$ be a D1207: Complex number.

Then \begin{equation} \cos z = \frac{e^{i z} + e^{- i z}}{2} \end{equation}

Formulation 1

Let $\cos$ be the D165: Standard complex cosine function.
Let $z \in \mathbb{C}$ be a D1207: Complex number.

Then \begin{equation} \cos z = \frac{\exp(i z) + \exp(- i z)}{2} \end{equation}