A complex number for which both and are integers. For example, , , , and are all Gaussian integers.

a complex number The complex numbers are an extension of the real numbers, in which all non-constant polynomials have roots

a complex number where and are integers

a complex number with integer real and imaginary parts

a generalization of integers into the complex plane

A Gaussian integer is a complex number whose real and imaginary part are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z[i]. This domain cannot be turned into an ordered ring, since it contains a square root of −1.