Gaussian integer

Complex number whose real and imaginary parts are both integers

In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z [ i ] {\displaystyle \mathbf {Z} [i]} or Z [ i ] . {\displaystyle \mathbb {Z} [i].} Gaussian integers share many properties with integers: they form a Euclidean domain, and thus have a Euclidean division and a Euclidean algorithm; this implies unique factorization and many related properties.

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