Eulers Identity?

Algebra Level 2

e i π + 1 = 0 \large e^{i\pi} + 1 = 0

So if you literally look up Eulers identity in Wikipedia or in your browser, you’ll know that e i π + 1 = 0 e^{i\pi} +1=0 . Using that, what should e i π + 2 = ? e^{i\pi} + 2 =\ ?

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Neil Patrao by Neil Patrao , 21, Australia

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3 solutions

e i π = cos ⁡ π + i sin ⁡ π = − 1 ⟹ e i π + 2 = − 1 + 2 = 1 e^{iπ}=\cos π+i\sin π=-1\implies e^{iπ}+2=-1+2=\boxed 1 .

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Lâm Lê
Sep 4, 2020

e i π + 2 = e i π + 1 + 1 = 0 + 1 = 1 e^{i\pi}+2=e^{i\pi}+1+1=0+1=1

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Neil Patrao
May 25, 2020

It’s pretty simple. If e to the iπ + 1=0, add one more and that’s e to the iπ +(1+1)=1 or e to the iπ + 1 = 0 + 1 =1

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