High Quality Content by WIKIPEDIA articles! In algebra, a conjugate of an element in a quadratic extension field of a field K is its image under the unique non-identity automorphism of the extended field that fixes K.Forming the sum or product of any element of the extension field with its conjugate always gives an element of K. This can be used to rewrite a quotient of numbers in the extended field so that the denominator lies in K, by multiplying numerator and denominator by the conjugate of the denominator. This process is called rationalization of the denominator, in particular if K is the field Q of rational numbers.

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