Quadratic Field
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Quadratic Field

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High Quality Content by WIKIPEDIA articles! In mathematics, a quadratic field is an algebraic number field K of degree two over Q. It is easy to show that the map d Q( d) is a bijection from the set of all square-free integers d 0,1 to the set of all quadratic fields. If d 0 the corresponding quadratic field is called a real quadratic field, and for d 0 an imaginary quadratic field or complex quadratic field, corresponding to whether its archimedean embeddings are real or complex. Quadratic fields are a basic object of study and class of examples in algebraic number theory. They have been stud...