Algebraic conjugate

In algebra, the conjugate of a binomial is another binomial formed by negating the second term of original binomial. The conjugate of x + y is x − y, where x and y are real numbers. If y is imaginary, the process is termed complex conjugation: the complex conjugate of a + bi is a − bi, where a and b are real.

In a commutative ring, an expression of the form

can be factored to give

where one factor is the conjugate of the other. This can be useful when trying to rationalize a denominator containing radicals.

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