"The complex numbers provide a particularly striking example for the foregoing. Certainly, nothing in our experience suggests the introduction of these quantities."
Written in an era long before 3d graphics and spatial navigation systems. Quaternions are just so darn useful that if we stubbornly insisted on not inventing complex numbers, we'd none the less end up with a magical set of manipulations that implement them without understanding them, and inevitably someone would look at those peculiar mechanical arithmetic steps and "invent" complex numbers.
Actually there are alternatives to thinking of them as complex numbers, specifically geometric algebra. Depending on who you believe, GA may be a better "design" of math for geometric calculations.
http://www.mrao.cam.ac.uk/~clifford/introduction/intro/intro...
Written in an era long before 3d graphics and spatial navigation systems. Quaternions are just so darn useful that if we stubbornly insisted on not inventing complex numbers, we'd none the less end up with a magical set of manipulations that implement them without understanding them, and inevitably someone would look at those peculiar mechanical arithmetic steps and "invent" complex numbers.
(edited to add for a good time visit
http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotatio...
and read all about it)