[Ken H]

I did not know that.

[getitright]

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.