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.

, has the conjugate pair roots: and

If the coefficients of a polynomial are all rational, any irrational root will have a conjugate pair.

, has the conjugate pair roots: and