These are the laws for handling of quaternions, outlined briefly under that node, but they need a bit more explanation. i, j and k are three unique roots of -1, so:

i² = j² = k² = -1 = ijk

A bit of thought reveals that multiplying the three units in any order produces -1. However, in general, one must remember that multiplication is non-commutative for quaternions:

ij = k     jk = i     ki = j
ji = -k    kj = -i    ik = -j

That's all you need to know! Impress all your friends as you manipulate quaternions with ease.

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