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# Quaternions and Rotation

So far, quaternions have been fairly abstract, except that a pure quaternion is a vector, so it's just as useful as vectors are. Now let's define a quaternion that represents a rotation in three-dimensional space.

Again, it's helpful to look at complex numbers to get a general pattern, and then apply that pattern to quaternions. The following complex number represents a rotation in two-dimensional space:

Multiply this complex number by any point (also represented by a complex number) and the point is rotated around the origin by θrotation degrees. This complex number we've called crotate is normalized because for any angle ...

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