# Category:Definitions/Gaussian Rationals

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This category contains definitions related to Gaussian Rationals.

Related results can be found in Category:Gaussian Rationals.

### Definition 1

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:

- $a + b i: a, b \in \Q$

### 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**.

## Pages in category "Definitions/Gaussian Rationals"

The following 4 pages are in this category, out of 4 total.