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

Formulation F12294 on R425: Euler's formulas for a real variable

F12294

Formulation 1

Let $y \in \mathbb{R}$ be a D993: Real number.
Let $i$ be the D371: Imaginary number.

Then

(1)	\begin{equation} e^{i y} = \cos y + i \sin y \end{equation}
(2)	\begin{equation} e^{- i y} = \cos y - i \sin y \end{equation}