Verified answer

The first question to ask is what kind of sense would it make to raise e to the power of i. Well, if we're going assign a meaning to complex exponents it has to be consistent with the meaning for real exponents.

In Calculus 2 you learned (or will learn) about Taylor series (or Taylor expansions) of functions. A Taylor series is a series that is developed based on a function's derivatives, and you can check any calculus text for details. The Taylor expansion for e^x is:

e^x = 1 + x + (x^2)/(2!) + (x^3)/(3!) + ... + (x^n)/(n!) + ...

In this series if you replace x with ix, you get a surprising result: the series turns into the sum of two other Taylor series. You get the Taylor series for cos(x) and the Taylor series for i sin(x). Consequently,

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

Now evaluate this function at x = 2 pi, and you get the identity you wondered about.

Maybe it refers to Euler's formula (e^(i*x) = cos (x) + i*sin (x))??