The most beautiful equation in mathematics

In 1748, Leonhard Euler (pronounced "oy-lr") published his most famous formula, aptly called Euler's Formula:

This is true for any real number θ. Substituting θ = π into this equation gives the most beautiful equation in math, called Euler's identity:

It is hard to overstate the beauty of this equation. It combines in one equation what are arguably the most important symbols and operations in mathematics. Along with the operations of addition, multiplication, and exponentiation, you have 0, the additive identity, 1, the multiplicative identity, i, the imaginary unit, and two of the most important mathematical constants, e and π. This equation is also integral to quantum computing. You will see eiθ all over the place in quantum computing, so you better get used to it!

So, how does this equation help us in quantum computing? You're about to find out, but first, we need...