# imaginary quadratic field

A quadratic number field $\mathbb{Q}(\sqrt{d})$, where $d$ is a negative squarefree^{} integer, is called a imaginary quadratic field^{}.

The name may be thought to describe the fact that such a quadratic field “imaginary numbers^{}” (in the sense ‘non-real complex numbers^{}’).

Other quadratic fields are real quadratic fields.

Title | imaginary quadratic field |

Canonical name | ImaginaryQuadraticField |

Date of creation | 2013-03-22 17:58:21 |

Last modified on | 2013-03-22 17:58:21 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 8 |

Author | pahio (2872) |

Entry type | Definition |

Classification | msc 11R11 |

Classification | msc 11R04 |

Synonym | quadratic imaginary field |

Synonym | imaginary quadratic number field |

Synonym | quadratic imaginary number field |

Synonym | imaginary quadratic extension |

Related topic | Imaginary |

Related topic | UnitsOfQuadraticFields |

Related topic | QuadraticImaginaryEuclideanNumberFields |

Related topic | ListOfAllImaginaryQuadraticPIDs |

Defines | real quadratic field |