University⏱ 4 min

Euler's Formula

e^(iπ) + 1 = 0

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1-1i-icos 60°sin 60°e^iπ=-1
θ = 60°
ei heta=cos⁡ heta+isin⁡ hetae^{i\ heta} = \cos\ heta + i\sin\ heta
ei⋅60°=0.500+0.866ie^{i \cdot 60°} = 0.500 + 0.866i

The most beautiful formula in math

eiπ+1=0e^{i\pi} + 1 = 0

(at θ = π, e^iπ = -1, so e^iπ + 1 = 0)

e^(iθ) is a point on the unit circle at angle θ. Increase θ and the point traces the circle. Euler's formula connects exponentials to trigonometry.