Definition:Conjugate Quaternion/Ordered Pair

Definition
Let $\mathbf x$ be a quaternion defined as an ordered pair $\left({a, b}\right)$ of complex numbers.

The conjugate quaternion of $\mathbf x$ is defined as:
 * $\overline {\mathbf x} = \overline {\left({a, b}\right)} = \left({\overline a, -b}\right)$