ld be magnitudes are negative numbers or angles are out of their natural
        ranges, as symmetries and periodicities kick in.
      </p>
<p>
        In this version of our implementation of quaternions, there is no analogue
        of the complex value operation <code class="computeroutput"><span class="identifier">arg</span></code>
        as the situation is somewhat more complicated. Unit quaternions are linked
        both to rotations in <span class="emphasis"><em><span class="bold"><strong>R<sup>3