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Sketching EM Waves with imaginary amplitudes

  1. Nov 2, 2008 #1
    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. jcsd
  3. Nov 2, 2008 #2

    gabbagabbahey

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    Gold Member

    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).
     
  4. Nov 2, 2008 #3
    ah thankyou! eulers identity... i should have known!
     
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