Complex Representation of Moving EM Waves

[rsaad]

Homework Statement

Moving in negative x-axis: E1 = E sin(wt + kx)
Moving in right axis: E2 = Esin(wt-kx-θ) moving to right

write complex representation

The Attempt at a Solution

E1= E Im(exp[i*(wt+kx)])
E2= E Im(exp[i*(wt-kx-θ)])

are these correct or do I have to take into account the -i^{^} for moving to left in E1?

 

[haruspex]

As I understand it, the advantage of writing the wave function in complex form is that a single complex constant encapsulates both the amplitude and the phase. So you should get equations without a separate constant for phase. See e.g. http://farside.ph.utexas.edu/teaching/315/Waves/node72.html