Definitions
from The Century Dictionary.
 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.
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics Describing any of several types of higher
dimensional numbers having some characteristics ofcomplex numbers.
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
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Examples

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

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

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.
Women Behind Bars 2009

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

Plants and trees are hypercomplex, like the climate.
Pathological Science... GayandRight 2007

Plants and trees are hypercomplex, like the climate.
Archive 20071101 GayandRight 2007

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 ...
Chapter 4 1990

"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?"
The Ghosts of Gol Mahr, Kurt 1976

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.
A Case Of Conscience Blish, James 1953
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