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Derivation

The equation appears in Leonhard Euler's Introduction, published in Lausanne in 1748. The identity is a special case of Euler's formula from complex analysis, which states that

$e^{ix}=\cos x+i\sin x\,\!$

for any real number $x$. If $x=\pi$, then

$e^{i\pi }=\cos \pi +i\sin \pi \,\!$

and since, by definition

$\cos \pi =-1\,$

and

$\sin \pi =0\,$

it follows that

Notes

Template:Ent Maor, p. 160. Maor cites Edward Kasner and James Newman's, Mathematics and the Imagination, New York: Simon and Schuster (1940), pp. 103–104, as the source for this quote. Template:Ent Feynman p. 22-10.