Particularly in the realm of complex numbers and irrational numbers, and more specifically when speaking of the roots of polynomials, a conjugate pair is a pair of numbers whose product is an expression of real integers and/or including variables. A complex number example: , a product of 13 An irrational example: , a product of 1. Or: , a product of -25. Often times, in solving for the roots of a polynomial, some solutions may be arrived at in conjugate pairs. If the coefficients of a polynomial are all real, for example, any non-real root will have a conjugate pair.