complex exponential signal periodicity

May 2010
I am used to identifying and proving periodic signals in the form: \(\displaystyle x[n] = 3cos(\frac{5n}{7} + \frac{ \pi }{4})\) with the 'rational/irrational'
method and also getting the fundamental period.

When it comes to this from: \(\displaystyle x(t) = e^{(-2+j( \frac{ \pi }{4} ))t} \) I am not sure how to prove it mathematically. I know that it is a signal with
an envelope function because of the exponential coefficient.

The only step I did for making the signal more clear is: \(\displaystyle x(t) = e^{-t}[cos \frac{ \pi t }{4} +jsin \frac{ \pi t}{4}]\)