I was reading a little more about Eisenstein and his contributions to mathematics, and I saw the following: An Eisenstein integer is a complex number of the form $z = a + b\omega$, where $\omega = \frac{1}{2}(-1 + i\sqrt 3) = e^{2\pi i/3}$. Apparently, $\omega$ is a cube root of unity, which basically means that $\omega ^{3}$ = 1. Eisenstein integers form a triangular lattice in the complex plane. The standard a+bi form that we use with complex numbers is actually called a "Gaussian integer." If we look at the complex plane of Gaussian integers, we will see the standard square lattice that we are used to. I found it interesting that there are different forms used for complex numbers- I was only familiar with Gaussian integers. For more information, check out the article on wikipedia: http://en.wikipedia.org/wiki/Eisenstein_integers

Eisenstein Integers