Examples for

Quaternions

Quaternions are a four-dimensional number system that is an extension of the field of complex numbers. Multiplication of quaternions is non-commutative in that the order of elements matters. A quaternion can be visualized as a rotation of vectors in three dimensions.
Quaternions

Compute and perform operations on quaternion expressions.

Get information about a quaternion:

quaternion: 0+2i-j-3k

Compare quaternions:

Quaternion(+11/11,-2,3,2), Quaternion(11,-2,0,-2)

Do calculations with quaternions:

quaternion -Sin[Pi]+3i+4j+3k multiplied by -1j+3.9i+4-3k
norm of quaternion 1+3i+4j+3^5k
conjugate: 1+3i+4j+3k, 1-1i-j+3k
inverse of quaternion 1+0i+0j+2k ** (-1i+3+4j+3k)

Visualize a quaternion:

draw 1+0i+5j+2k as a rotation operator
More examples