Euler’s identity is a special case of Euler’s formula from complex analysis, which states that for any real number x,
e^{ix} = \cos x + i\sin x
where the inputs of the trigonometric functions sine and cosine are given in radians.
In particular, when x = π, or one half-turn (180°) around a circle:
e^{i \pi} = \cos \pi + i\sin \pi.
Since
\cos \pi = -1 \, \!
and
\sin \pi = 0,
it follows that
e^{i \pi} = -1 + 0 i,
which yields Euler’s identity:
e^{i \pi} +1 = 0.
That was going to be my guess...
That was going to be my guess...
Damn! I dated that Euler chick in college.
I’ll take your word for it FRiend.
OH YEAH? Well nickcarraway is right, Han DID shoot first!