Editing Gaussian integer (section)

==Gaussian rationals==
The [[field (mathematics)|field]] of [[Gaussian rational]]s is the [[field of fractions]] of the ring of Gaussian integers. It consists of the complex numbers whose real and imaginary part are both [[rational number|rational]].

The ring of Gaussian integers is the [[integral closure]] of the integers in the Gaussian rationals.

This implies that Gaussian integers are [[quadratic integer]]s and that a Gaussian rational is a Gaussian integer, if and only if it is a solution of an equation
:<math>x^2 +cx+d=0,</math>
with {{math|''c''}} and {{math|''d''}} integers. In fact {{math|''a'' + ''bi''}} is solution of the equation
:<math>x^2-2ax+a^2+b^2,</math>
and this equation has integer coefficients if and only if {{math|''a''}} and {{math|''b''}} are both integers.