Gaussian number

The **Gaussian numbers**, sometimes (unnecessarily) called the **Gaussian rational numbers**, are the elements of the number field $\mathbb{Q} + \mathrm{i}\mathbb{Q}$, where $\mathbb{Q}$ is the field of rational numbers. In other words, a complex number is Gaussian (and a fortiori algebraic) iff both its real and imaginary parts are rational. The **Gaussian integers** are the algebraic integers in the Gaussian numbers, which happen to be simply the elements of the integral domain $\mathbb{Z} + \mathrm{i}\mathbb{Z}$, where $\mathbb{Z}$ is the integral domain of (rational) integers.

Revised on April 1, 2012 10:35:52
by Urs Schreiber
(89.204.139.110)