Consider a harmonic electromagnetic plane wave with angular frequency o and propagation vector k=(kx,ky,kz) (i.e., propagating in an arbitrary direction). The electric field vector is E=(Ex,Ey,Ez) with amplitudes (Exo, Eyo, Ezo) and the magnetic field vector is B=(Bx,By,Bz) with amplitudes (Bxo, Byo, Bzo). a) Write an expression for the electric and magnetic waves using complex representation. b) Using the laws of electromagnetism without sources (Maxwell's equations in free space), prove that k x E = @B, and k . E = 0. c) What does part b) tell you about the relative directions of k, E and B