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# 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 contains “imaginary numbers” (in the sense ‘non-real complex numbers’).

Other quadratic fields are real quadratic fields.

Defines:

real quadratic field

Related:

Imaginary, UnitsOfQuadraticFields, QuadraticImaginaryEuclideanNumberFields, ListOfAllImaginaryQuadraticPIDs

Synonym:

quadratic imaginary field, imaginary quadratic number field, quadratic imaginary number field, imaginary quadratic extension

Type of Math Object:

Definition

Major Section:

Reference

Parent:

Groups audience:

## Mathematics Subject Classification

11R11*no label found*11R04

*no label found*

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