# Gaussian Integer

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

Gaussian integer is a college-level concept that would be first encountered in an abstract algebra course covering rings and fields.

### Examples

i: |
i is the symbol used to denote the principal square root of -1, also called the imaginary unit. |

### Prerequisites

Algebraic Number: | An algebraic number is a number that is the root of some polynomial with integer coefficients. Algebraic numbers can be real or complex and need not be rational. |

Complex Number: | A complex number is a number consisting of a real part and an imaginary part. A complex number is an element of the complex plane. |

Field: | A field is a ring in which every nonzero element has a multiplicative inverse. The real numbers and the complex numbers are both fields. |

Integer: | An integer is one of the numbers ..., -2, -1, 0, 1, 2, .... |