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r^{2}= (x-a)^{2}+ (y-b)^{2}+ (z-c)^{2}

can generally represent displacement,

why can

r^{2}= (x- ia)^{2}+ (y- ib)^{2}+ (z- ic)^{2}

generally represent rotation?

(i^{2}= -1)

And why

r^{2}= x^{2 }+ y^{2}+ (z - ia)^{2}

represents rotation with respect to z axis

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# Can this represent rotation? Why?

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