# Sketching EM Waves with imaginary amplitudes

1. Nov 2, 2008

### hutchwilco

1. The problem statement, all variables and given/known data
Sketch in 3D, the following waves. (both E fields are in x direction
E_1 = 3*exp(-j*8*Pi*z)
E_2 = 4j*exp(-j*8*Pi*z)

(where j=sqrt(-1)

3. The attempt at a solution

I know how to sketch E_1, but my question is how to treat the imaginary amplitude, 4j in E_2.
here is my stab at it: the amplitude is really of form (a+jb) but with no real component.
ie 0 +4j. but how to sketch this?
but I can't find any conclusive info in my text book or lecture notes on how to sketch this - do i just draw the wave as normal and say the max amplitude is "4j" ? this doesn't seem right to me since you can't have a 4j E field in reality so you shouldn't be able to sketch one!
if I do this, how then do i combine waves as a follow up question may be sketch E_1 + E_2

Last edited: Nov 2, 2008
2. Nov 2, 2008

### gabbagabbahey

You are only going to be able to sketch the real part of the function...for E_1, that's 3cos(8*Pi*z), for E_2, euler's identity gives 4j*exp(-j*8*Pi*z)=4j[cos(8*Pi*z)-j*sin(8*Pi*z)]=[4jcos(8*Pi*z)+4sin(8*Pi*z)] and so the real part is just 4sin(8*Pi*z).

3. Nov 2, 2008

### hutchwilco

ah thankyou! eulers identity... i should have known!