# The Quaternion Product

High school teachers teaching vector operations refer to the three unit vectors i, j, and k, but probably don't realize where they come from.
Quaternions are a number system that extends the complex numbers by introducing three quaternion units i, j, and k. A quaternion is the sum of a real number and real multiples of these quaternion units,

*q*=*w*+*xi*+*yj*+*zk*. Quaternion multiplication is non-commutative.## Inspired by this blog post

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