Exponential formulation of waves

[11thHeaven]

Hi all, I'd just like to clear up something that's often confused me.

In classes (particularly classical waves/QM) we've often seen the lecturer switch from describing a wave as (most commonly) $$Acos(kx-{\omega}t)$$ to $$e^{i(kx-{\omega}t)}$$
but doesn't the exponential representation include an imaginary sine term as well? Shouldn't this given wave be represented as ( $$Re [e^{i(kx-{\omega}t)}]$$)?

If this is the case, is it just a convention that the "Re" is dropped?

Thanks.

 

[Pythagorean]

As far as I've seen, yes, it's just convention.

 

[Redbelly98]

For classical waves (like E-M waves), yes, it's generally understood that the real part of the expression gives the physical wave (like the electric field value).

For wavefunctions in quantum mechanics, the imaginary part is really part of the wavefunction. All the operations used to find an observable quantity (energy, momentum, probability) from the complex wavefunction still give real-valued results.