Definition:Conjugate Quaternion/Ordered Pair

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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:

$\overline {\mathbf x} = \overline {\left({a, b}\right)} = \left({\overline a, -b}\right)$


Sources