Definition:Conjugate of Quadratic Irrational

Definition
Let $\alpha = r + s \sqrt n$ be a quadratic irrational.

Then its conjugate is defined as:
 * $\tilde \alpha = r - s \sqrt n$

Thus $\alpha$ and $\tilde \alpha$ are known as conjugate quadratic irrationals.

Notation may vary.

Also known as
A pair of conjugate quadratic irrationals can be referred to as conjugate quadratic surds or just conjugate surds.