Now I understand how natural numbers work and the basics of complex numbers like i and i\^4 and stuff. But what is a hypercomplex number? I’ve tried searching google but I always had no idea what it was talking about. There are even things like quaternions and octonions, like what is that?
In: Mathematics
i*i is defined as -1.
Quaternions etc just define j*j as also -1, and k*k as -1 but then they also define i*j=k, and k*j=-i. In doing so they make a number system with useful properties, especially for rotations.
But if you are looking for a “real” thing, they are just defined to be the way they are to be useful.
Latest Answers