How would I find the magnitude of this wave.(complex numbers/quanties)

[zumbo1]

ψ(y,t)=2*e^(iky)*e^(iωt) + 4*e^(iky)*e^(-iωt)
Here is my work for the problem
2e^(iky)*(e^(iωt)+2e^(-iωt)); 2e^(iky)*(cos(ωt)+i*sin(ωt)+2cos(ωt)-2i*sin(ωt));
2e^(iky)*(3cos(ωt)-isin(ωt))
How would you continue this problem?

 

[Galileo]

You are asked for the absolute value (or magnitude) of 2e^{iky}(3\cos(\omega t)-i\sin(\omega t)).
I'm sure you know how to calculate the magnitude of a complex number.
The magnitude will depend on time.

 

[cepheid]

My advice would be to rewrite the wave in the form:

\Psi(y,t) = 2e^{i(ky + \omega t)} + 4e^{i(ky - \omega t)}

and it should be obvious from this form that you have the sum of two sinusoidal waves, one traveling to the left (er, negative y-direction) with amplitude 2, and the other to the right (+ y-direction) with amplitude 4. If that is not obvious, then consider that if this is really a physical wave propagating along the y-axis, then the physical wave is given by:

Re[\Psi(y,t)] = 2\cos{(ky + \omega t)} + 4\cos{(ky - \omega t)}

To be honest, I'm not sure how/don't feel like putting in the effort at this hour to calculate the combined amplitude of the two waves, and whether that corresponds to the magnitude of the complex number psi.

Edit, just saw Galileo's post, so maybe I was way off on this one/answering the wrong question.

 

[zumbo1]

How do you edit posts?
Anyway I end up getting (20+16cos(wt))^1/2 for my magnitude.

 

[Galileo]

The magnitude of 2e^{iky}(3\cos(\omega t)-i\sin(\omega t)) is not \sqrt{20+16\cos(\omega t)}.
Try again.

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