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