We are all familiar with splitting natural numbers into prime components. This decomposition is unique, except for the order of the factors. We can apply the idea of prime components to many more general sets of numbers.
The Gaussian integers are all the complex numbers with integer real and imaginary parts, that is, all numbers in the set
The set forms a two-dimensional lattice in the complex plane. For any element
we consider the four numbers
as associates. The associates of
are known as units:
.