In mathematics, the conjugate of an expression of the form is provided that does not appear in a and b. One says also that the two expressions are conjugate.
In particular, the two solutions of a quadratic equation are conjugate, as per the in the quadratic formula .
Complex conjugation is the special case where the square root is the imaginary unit.
As and the sum and the product of conjugate expressions do not involve the square root anymore.
This property is used for removing a square root from a denominator, by multiplying the numerator and the denominator of a fraction by the conjugate of the denominator (see Rationalisation). An example of this usage is: Hence:
A corollary property is that the subtraction:
leaves only a term containing the root.