Math 2.0

statement corollary

Euler's identity

Statement

eiπ+1=0.e^{i \pi} + 1 = 0.

Remarks

Proof: Euler's formula with z=πz = \pi gives eiπ=cos⁡π+isin⁡π=−1e^{i \pi} = \cos \pi + i \sin \pi = -1. The identity links five constants: 00, 11, π\pi, ee and ii.

Explanations

L1 human

Walk around the unit circle from 11 for a distance of π\pi, which is half of the circle. You arrive at −1-1, so eiπ=−1e^{i \pi} = -1.

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Sources

  1. Web https://en.wikipedia.org/wiki/Euler%27s_identity, lead section

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