i x is x rotated left by pi/2 df/dx = f df(ix)/dx = i f (ix) so the "velocity" is always orthogonal to the "position". Thus the solution to this equation in

i x is x rotated left by pi/2 df/dx = f df(ix)/dx = i f (ix) so the "velocity" is always orthogonal to the "position". Thus the solution to this equation in the complex numbers has to be a rotation.