Consider a right circularly polarized wave with electric field amplitude under root 2 Er, and a left circularly polarized wave with amplitude under root 2 El, which have tha same frequency w. (a) If both waves travel through a plasma along a uniform magnetic field which is oriented in the z-direction. Show that the total electric fields E=[ex {Er exp (iKrz)+El exp (iKlz) + iey}Er (iKrz)-El exp (iKlz) }]exp (-iwt) where Kr and Kl are given by 

Kr= w/c {1+W^2pe/w (Wce-w)}^1/2

Kl= w/c {1-Wpe/w (Wce+w)

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