Definition:Gaussian Integer
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Definition
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 $\Z \left[{i}\right]$, and hence can be defined as:
- $\Z \left[{i}\right] = \left\{{a + b i: a, b \in \Z}\right\}$
Some sources use the symbol $J$ for the set $\Z \left[{i}\right]$.
Source of Name
This entry was named for Carl Friedrich Gauss.
Sources
- B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra (1970): $\S 1.2$: Ring Example $5$
