Complex notation of periodic functions

[Apteronotus]

I have found in physics literature a periodic function of time is many times written in complex form.
For example,

$$f(x,t)=g(x)e^{i\omega t}$$
​

As a non-physicist this has proven a bit confusing.

Is it generally understood that the function we are really interested in the real part of the complex?
ie.

$$Re(g(x)e^{i\omega t})$$​

Is the reason for the complex format for simplification when the equation is manipulated?

Thanks,

 

[Vanadium 50]

Often we are interested in the real part of the complex variables. Sometimes the real part is one physical variable and the imaginary part (Remember, Im(z) is a *real* number) is another one. When this fortunate situation arises, we can solve two problems at once.

 

[Apteronotus]

Thank you Vanadium. Very well explained!