# 欧拉恒等式

e0 = 1开始，以相对速度i,走π长时间，加1，则到达原点。

${\displaystyle e^{i\pi }+1=\,}$${\displaystyle 0}$

## 证明

${\displaystyle e^{ix}=\cos x+i\sin x\,\!}$欧拉公式
${\displaystyle e^{i\pi }=\cos \pi +i\sin \pi \,}$（代入${\displaystyle x=\pi \,}$
${\displaystyle e^{i\pi }=\,}$${\displaystyle -1}$（因${\displaystyle \cos \pi =-1\,\!}$${\displaystyle \sin \pi =0\,\!}$
${\displaystyle e^{i\pi }+1=\,}$${\displaystyle 0}$

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