Euler's identity

probably the most beautiful equation in all mathematics.

Étiquette

\begin{aligned} e^{i \pi} &+ 1 = 0 \\ \\ \because e &: \text{Euler's number} \\ i &: \text{imaginary unit satisfies } i^{2} = -1 \\ \pi &: \text{pi} \end{aligned}

Special case of Euler’s formula:

e^{i \theta} = \cos(\theta) + i \sin(\theta)

\begin{aligned} e^{i \pi} &+ 1 = 0 \\ \\ \because e &: \text{Euler's number} \\ i &: \text{imaginary unit satisfies } i^{2} = -1 \\ \pi &: \text{pi} \end{aligned}

Special case of Euler’s formula:

e^{i \theta} = \cos(\theta) + i \sin(\theta)