>>56
It obviously has real numbers for an area. In the normal cartesian plane we have real numbers for areas, you've just mapped everything from this plane, to a plane where the axis have been multplied through by i.
It trivially follows that areas in this plane, are just the additive inverse of the areas in the other plane.
Do you know what a jacobian is?
You've basically described a transformation x->u=ix and y->v=iy
the jacobian of this transformation is what areas are scaled by and is the determinant of the jacobian matrix
( du/dx dv/dx)
( ) at least I hope I'm remembering this shit right
(du/dy dv/dy)
anyway, that's pretty obviously i*i=-1.
Hence the negative area thing makes perfect mathematical sense.
Again, not sure how more succinctly to describe this.