\begin{definition}[Definition:Gaussian Rational/Definition 2]
The field $\sqbrk {\Q \sqbrk i, +, \times}$ of '''Gaussian rationals''' is the field of quotients of the integral domain $\struct {\Z \sqbrk i, +, \times}$ of Gaussian integers.
This is shown to exist in Existence of Field of Quotients.
In view of Field of Quotients is Unique, we construct the field of quotients of $\Z \sqbrk i$, give it a label $\Q \sqbrk i$ and call its elements '''Gaussian rationals'''.
\end{definition}