Definition:Gaussian Rational

A Gaussian rational is a complex number whose real and imaginary parts are both rational numbers.

That is, a Gaussian rational is a number in the form:
 * $$a + b \imath: a, b \in \Q$$

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