Unitary 1, imaginary unit I, and J and K. Of course, this is just a symbol. Mainly its operation meets the following requirements:

1* 1= 1， 1*i=i， 1*j=j， 1*k=k

i^2=j^2=k^2=- 1

ij=k，ik=-j，ji=-k，jk=i，ki=j，kj=-i

(If you remember, you can use the cross product operation of three basis vectors in three-dimensional space to remember. )

It can be seen immediately that \mathbb H={ 1, i, j, k} constitutes a noncommutative associative algebra.

Since the complex set \mathbb C is actually a set of binary numbers, we can think that \mathbb C is a subset of \ mathbbc in the sense of isomorphism.

There is a history here. Shortly after the binary number came out, the ternary number came out and the quaternary number didn't come out. It is said that Hamilton spent ten years constructing quaternions, and he began to devote himself to commutativity, but it has been fruitless. Once a meeting passed by a bridge, he had a brainwave, gave up commutativity and constructed quaternion.