Consider a plane wave that is a superposition of two independent orthogonal plane waves that can be written as the real part of \vec{E} = E_1\exp\left[i\left(kz-\omega t\right)\right]\hat{i} + E_1 \exp\left[i\left(kz-\omega t + \pi\right)\right]\hat{j}E → = E 1 exp ⁡ [ i ( k z − ω t ) ] i ^ + E 1 exp ⁡ [ i ( k z − ω t + π ) ] j ^ where LaTeX: k,\,\omega,\,E_1,\textrm{ and }E_2k , ω , E 1 , and E 2 are all real. If E_1 = E_2, the tip of the electric field vector will describe a trajectory that, as viewed along the z-axis from positive z and looking toward the origin, is a