# 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.

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

### Examples

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

Rational Number: | A rational number is a real number that can be written as a quotient of two integers. |

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

### Prerequisites

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. |

Polynomial: | A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. |