Eisenstein integers

Eisenstein integers are a special type of complex numbers used in advanced mathematics, particularly in number theory. They are represented as numbers of the form \( a + b \cdot \omega \), where \( a \) and \( b \) are regular integers, and \( \omega \) is a complex cube root of unity, specifically \( \omega = \frac{-1 + \sqrt{3}i}{2} \). This means Eisenstein integers can be plotted on a plane similar to regular numbers but are arranged in a triangular lattice. They have unique properties that make them useful in studying algebraic integers and factoring.