\begin{definition}[Definition:Conjugate of Quadratic Irrational]
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.
\end{definition}