Can this represent rotation? Why?

yicong2011

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