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    Gaussian Integer

    Basic definition

    A Gaussian integer is a complex number a + b i, where a and b are integers and i is the imaginary unit.

    Detailed definition

    A Gaussian integer is a complex number a + b i where a and b are integers. The Gaussian integers are members of the imaginary quadratic field Q(sqrt(-1)) and form a ring often denoted Z[i], or sometimes k(i). The sum, difference, and product of two Gaussian integers are Gaussian integers, but (a + b i)|(c + d i) only if there is an e + f i such that (a + b i)(e + f i) = (a e - b f) + (a f + b e) i = c + d i (Shanks 1993). Gaussian integers can be uniquely factored in terms of other Gaussian integers (known as Gaussian primes) up to powers of i and rearrangements.

    Related terms

    complex number | Eisenstein integer | Gaussian prime | integer | octonion

    Educational grade level

    college level

    Associated person

    Carl Friedrich Gauss

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