the perfect equation

it is perfect because it has all the five important numbers in math: pie, zero, one, i (square root of -1) and e.

The following shows how it is derived. The identity is a special case of Euler's formula from complex analysis, which states that

for any real number x. (Note that the arguments to the trigonometric functions sin and cos are taken to be in radians.) In particular,

Since

and

it follows that

which gives the identity