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

 

[fresh_42]

This makes no sense without further explanations. All of them are just equations which describe a surface in some Euclidean space. But here are some mappings which might help in this context:
https://www.physicsforums.com/insights/journey-manifold-su2mathbbc-part/