3. The electromagnetic wave equation for a wave that propagates along z-axis in the positive direction, and oscillates in the x-direction has the form: 2 O' E(x) "- E(x) o dE(x) = 6 + az2 at2 at where c is a constant, & is the dielectric constant, o is the conductivity, and go is the permittivity of vacuum. The general trial solution to this equation can be written as: zn E(x) = Ex exp in Using this expression show that index of refraction is generally a complex number, and derive its expression