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.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): conjugate surds