Category:Gaussian Rationals
This category contains results about Gaussian Rationals.
Definitions specific to this category can be found in Definitions/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 $\struct {\Q \sqbrk i, +, \times}$ 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 "Gaussian Rationals"
The following 2 pages are in this category, out of 2 total.