Maths - Quaternion Notations - Superset of complex numbers

A complex number may be expressed as the sum of a real and imaginary part as follows:

a + i b

A quaternion adds two additional and independent imaginary parts as follows:

a + i b + j c + k d


So this adds two extra dimensions which square to a negative number, giving a total of:

Representing Rotations

It does superficially look like quaternions extend the way that complex numbers represent rotations, but I don't think quaternion rotation is an extension the way complex numbers represent rotations, they are completely different. I think it is just a coincidence that they both happen to represent rotations. (if it is valid to use the word 'coincidence' in mathematics). For instance:



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