Definition:Gaussian Integer

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:
 * $$a + b \imath: a, b \in \Z$$

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