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I mean, quaternions are the weirder version of complex numbers, and they're used for calculating 3D rotations in a lot of production code.
There's also the octonions and (much inferior) Clifford algebras beyond that, but I don't know about applications.
Yeah but aren't quaternions basically just a weird subgroup of 2x2 complex matrices?
Would that make it less true? Complex numbers can be seen as a weird subgroup of the 2x2 real matrices. (And you can "stack" the two representations to get 4x4 real quaternions)
Furthermore, octonions are non-associative, and so can't be a subgroup of anything (although you can do a similar thing using an alternate matrix multiplication rule). They still show up in a lot of the same pure math contexts, though.