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Can this represent rotation? Why?

by yicong2011
Tags: imaginary numbers, rotation
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May1-11, 11:44 PM
P: 76
If we say

r2= (x-a)2 + (y-b)2 + (z-c)2

can generally represent displacement,

why can

r2= (x- ia)2 + (y- ib)2 + (z- ic)2

generally represent rotation?

(i2 = -1)

And why

r2= x2 + y2 + (z - ia)2

represents rotation with respect to z axis
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