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'Quaternions and Rotations' printed from https://nrich.maths.org/
Comparing the results in parts (1) and (2) we see that in part (1)
$q = \cos 45^o + \sin 45^o{\bf i}$ and the map $qvq^{-1}$ fixes the
x-axis and gives a rotation of twice 45 degrees about the x-axis.
The result in (2) is slightly more general showing that where $q =
\cos \theta + \sin \theta {\bf k}$ the map $q v q^{-1}$ fixes the
z-axis and gives a rotation of $2\theta$ about the z-axis. \par For
a more general account of quaternions and rotations see the
article....