Euler's Formula

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

e^{i\phi} = \cos \phi + i\sin \phi \!

Euler's Identity

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

e^{i\pi} + 1 = 0 \!

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

See also

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