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 6 subcategories, out of 6 total.
Pages in category "Gaussian Integers"
The following 16 pages are in this category, out of 16 total.
G
- Gaussian Integer Units are 4th Roots of Unity
- Gaussian Integer Units form Multiplicative Subgroup of Complex Numbers
- Gaussian Integers are Closed under Addition
- Gaussian Integers are Closed under Multiplication
- Gaussian Integers are Closed under Negation
- Gaussian Integers are Closed under Subtraction
- Gaussian Integers are not Closed under Division
- Gaussian Integers does not form Subfield of Complex Numbers
- Gaussian Integers form Euclidean Domain
- Gaussian Integers form Integral Domain
- Gaussian Integers form Principal Ideal Domain
- Gaussian Integers form Subgroup of Complex Numbers under Addition
- Gaussian Integers form Subring of Complex Numbers