Extracted from a beautiful identity

Algebra Level 2

e π i + 1 = ? \large e^{πi}+1 = \ ?

Details and Assumptions :

  • i i is an imaginary number such that i 2 = − 1 i^2 = -1 .


The answer is 0.

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Godwin Tom George by Godwin Tom George , 27, India

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3 solutions

Godwin Tom George
Mar 17, 2015

e i x e^{ix} = c o s x cos{x} + i i s i n x sin{x}

=> e i π e^{iπ} = c o s π cos{π} + i i s i n π sin{π} = − 1 -1 +0 = − 1 -1

=> e i π e^{iπ} +1 = 0

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Gagan Raj
Mar 17, 2015

Euler's Identity also known as Euler's God Equation. Mathematicians have proved this one but still nobody knows the practical aspect of this !!!!!

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. .
Feb 9, 2021

e π i + 1 = e π i ⇒ − 1 → e π i + 1 = − 1 + 1 = 0 e^{\pi i}+1 = e^{\pi i} \Rightarrow -1 \rightarrow e^{\pi i} + 1 = -1 + 1 = 0 .

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