To get an understanding of what a polarization state looks like, one can observe the orbit that is made if the polarization state is multiplied by a phase factor of e i ω ω t and then having the real parts of its components interpreted as x and y coordinates respectively. That is: ( x ( t ) y ( t ) ) = ( ℜ ℜ ( e i ω ω t ψ ψ x ) ℜ ℜ ( e i ω ω t ψ ψ y ) ) = ℜ ℜ [ e i ω ω t ( ψ ψ x ψ ψ y ) ] = ℜ ℜ ( e i ω ω t | ψ ψ ⟩ ⟩ ) .