# Category:Gaussian Integers

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This category contains results about Gaussian Integers.

Definitions specific to this category can be found in Definitions/Gaussian Integers.

A **Gaussian integer** is a complex number whose real and imaginary parts are both integers.

That is, a **Gaussian integer** is a number in the form:

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

The set of all **Gaussian integers** can be denoted $\Z \sqbrk i$, and hence can be defined as:

- $\Z \sqbrk i = \set {a + b i: a, b \in \Z}$

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### G

### U

## Pages in category "Gaussian Integers"

The following 9 pages are in this category, out of 9 total.

### G

- Gaussian Integer Units are 4th Roots of Unity
- Gaussian Integer Units form Multiplicative Subgroup of Complex Numbers
- Gaussian Integers does not form Subfield of Complex Numbers
- Gaussian Integers form Integral Domain
- Gaussian Integers form Subgroup of Complex Numbers under Addition
- Gaussian Integers form Subring of Complex Numbers