Conjugate (square roots)
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.
Properties[edit]
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.
See also[edit]
- Conjugate element (field theory), the generalization to the roots of a polynomial of any degree