Euler's Formula

Euler's formula is the following identity in complex analysis making use of the imaginary number <math>i</math>:

<math>e^{i\phi} = \cos \phi + i\sin \phi \!</math>

Euler's Identity

The formula can be used to derive an equation known as Euler's identity:

<math>e^{i\pi} + 1 = 0 \!</math>

This is called the most beautiful equation in all of mathematics, because it equates the five most common mathematical constants in a perfectly elegant manner.

See also

• De Moivre's Theorem
• Leonard Euler
• Arbitrariness or Ambiguity in the Definition of the Imaginary Unit in Mathematics