How to Understand Euler's Identity

Euler's Identity is e^i*pi = -1, where e is about 2.718, i is the square root of -1, and pi is about 3.14. 

The identity is an alternative form of Euler's Formula which is e^(i*x) = cos(x) + i*sin(x).

In the above equation, if we let x = pi, we get:

e^(i*pi) = cos(pi) + i*sin(pi)

Since the cos(pi) = -1 and sin(pi) = 0, we get:

e^(i*pi) = -1

Strange as it may seem, this identity is useful for solving equations about real quantities, particularly in electrical engineering. A phasor is an example of the use of i to describe real quantities, for example. 

This identity can also be used to solve differential equations of the form ax^2y'' + bxy' + cy = 0. These are called Euler equations. 

This is about as far as 99% of college students get with math, so I feel this is a good stopping point for my math series.