Conjugate (algebra)

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

Differences of squares[edit]

In a commutative ring, an expression of the form

 a^2-b^2

can be factored to give

 (a+b)(a-b)

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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