Complex sentence: This is the most complete representation of polarized electromagnetic radiation and corresponds in general to elliptical polarization, i.e., at a fixed point in space (or for fixed z), the electric vector\\ mathbf traces out an ellipse in the x-y plane.
Split into simpler sentences: This is the most complete representation of polarized electromagnetic radiation and corresponds in general to elliptical polarization. At a fixed point in space (or for fixed z), the electric vector\\ mathbf traces out an ellipse in the x-y plane.