Sketching EM Waves with imaginary amplitudes

[hutchwilco]

Homework Statement

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)

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 textbook 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

 

[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).

 

[hutchwilco]

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