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Gaussian integers are named after the German mathematician [[Carl Friedrich Gauss]].
[[File:Gaussian integer lattice.svg|thumb|217px|Gaussian integers as [[integer lattice point]]s in the [[complex plane]]]]
==Basic definitions==
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Since the Gaussian integers are closed under addition and multiplication, they form a [[commutative ring]], which is a [[subring]] of the field of complex numbers. It is thus an [[integral ___domain]].
When considered within the [[complex plane]], the Gaussian integers constitute the {{math|2}}-dimensional [[
The ''conjugate'' of a Gaussian integer {{math|''a'' + ''bi''}} is the Gaussian integer {{math|''a'' − ''bi''}}.
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Most of the unsolved problems are related to distribution of Gaussian primes in the plane.
*[[Gauss's circle problem]] does not deal with the Gaussian integers per se, but instead asks for the number of [[integer lattice point]]s inside a circle of a given radius centered at the origin. This is equivalent to determining the number of Gaussian integers with norm less than a given value.
There are also conjectures and unsolved problems about the Gaussian primes. Two of them are:
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