Demodulate an given AM signal?

Hi guys, new here.

I have an AM signal that is saved under a complex array format.

This is how it looks like. I tried to apply the demod function from Matlab but it said that it can not receive complex arguments.

So I applied a real(signal) function. After I have applied the demodulation on it.

But when I reverse the process it does not look the same like the initial signal.

I have seen examples on generated signals but my question is, can this kind of process be made on a given signal and not a mathematically generated one by the program?