Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Describing any of several types of higher dimensional numbers having some characteristics of complex numbers.
from The Century Dictionary and Cyclopedia
 Composed of a number of imaginaries or complex quantities. Thus, a quantity ai + bj + etc., where a, b, etc., are complex scalars, while i, j, etc., are peculiar units, having their proper multiplicationtable, is a hypercomplex quantity.
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

This means that if we represent a rotation around the vertical by some "hypercomplex" number

If hypercomplex systems were predictable, NASA would have foolproof space shuttles  because they are a lot simpler than the climate.

Many are hypercomplex and rely on rare ingredients that few of us would have any luck finding  but again, this is par for the course in the world of culinary cocktails.

Plants and trees are hypercomplex, like the climate.

If hypercomplex systems were predictable, NASA would have foolproof space shuttles — because they are a lot simpler than the climate.

A quaternion is, in fact, a generalized or hypercomplex number ...

"You know the formalism of your mathematics which defines a particle and converts it into an antiparticle simply by rotating the hypercomplex system of coordinates?"

And perhaps he had seen, too, that the time Ruiz%Sanchez had devoted to the elaborate, capriciously hypercomplex case of conscience in the Joyce novel had been time wasted; there was a much simpler case, one of the classical situations, which applied if Ruiz%Sanchez could only see it.

My guess is that the health care "industry" will unravel in the years ahead under the weight of its own hypercomplexity just as all the other hypercomplex systems of normal American life

Yes, we realize it's odd to evoke football whilst discussing a band as ethereal as iNFiNiEN, but consider this: Hollenberg, who doubles in the hypercomplex grindcore group Cleric, comes at music from a metal and psychedelic background.
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