A system x(t) (Continuous Time) is periodic if T>0 such that x(T+t) = x(t). A system x[n] (Discrete Time) is periodic if there exists N integer>0 such that x[n+N] = x[n]
Not all complex exponentials are periodic.
Here is an example of a periodic system:
e^((1/4)j*pi*n) is periodic because: wo=(1/4)pi , wo/(2pi)=(1/8) which is a rational number
Here is an example of a non-periodic system:
e^(sqrt(3)j*pi*n) is not periodic because: wo=(sqrt(3)pi) , wo/(2pi)= (sqrt(3)/2) which is not a rational number
