e and His Imaginary Friend

Euler's Equation

The square root of -1, i, is an imaginary number, so that

e^ix = cos(x) + i sin(x).

This is Euler’s equation, which is a very useful identity to use to avoid working with imaginary numbers coupled with trigonometric functions.

The following identity is one which relates what some refer to as the "famous five" numbers, e, π, i, 1, and 0.

e^iπ + 1= 0

This equation is easy to prove by substituting pi for x in Euler’s equation mentioned above.