Dirkjan: Created page with " $e^i\pi +1 = 0$ The identity is a special case of Euler's formula from complex analysis, which states that $e^{ix} = \cos x + i \sin..."$

2020-08-25T08:18:16Z

Created page with "<math> e^i\pi +1 = 0 </math> The identity is a special case of Euler's formula from complex analysis, which states that <math> e^{ix} = \cos x + i \sin..."

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

The identity is a special case of [[Eulers formula|Euler's formula]] from complex analysis, which states that

<math> e^{ix} = \cos x + i \sin x \,\!</math>

for any real number x. (Note that the arguments to the trigonometric functions sin and cos are taken to be in radians.) In particular,

<math> e^{i \pi} = \cos \pi + i \sin \pi.\,\!</math>

Since

<math> \cos \pi = -1 \, \! </math>

and

<math> \sin \pi = 0,\,\!</math>

it follows that

<math> e^{i \pi} = -1,\,\!</math>

which gives the identity

<math> e^{i \pi} +1 = 0.\,\! </math>
[[Category:microscopy]]

Eulers identity - Revision history

Dirkjan: Created page with " e^i\pi +1 = 0 The identity is a special case of Euler's formula from complex analysis, which states that e^{ix} = \cos x + i \sin..."

Dirkjan: Created page with " $e^i\pi +1 = 0$ The identity is a special case of Euler's formula from complex analysis, which states that $e^{ix} = \cos x + i \sin..."$