Definition:Gaussian Integer

Definition
A Gaussian integer is a complex number whose real and imaginary parts are both integers.

That is, a Gaussian integer is a number in the form:
 * $a + b i: a, b \in \Z$

The set of all Gaussian integers can be denoted $\Z \left[{i}\right]$, and hence can be defined as:
 * $\Z \left[{i}\right] = \left\{{a + b i: a, b \in \Z}\right\}$

Some sources use the symbol $J$ for the set $\Z \left[{i}\right]$.