Here is an example of a periodic function:
$ y = j e^{j 10 t} $
$ = j(\cos 10t + j \sin 10t) $
$ = j \cos 10t - \sin 10t $
When t = 0, y = j. We know that $ \cos $ and $ \sin $ have the same values when evaluated at 0 and $ 2\pi $. So, $ 10t = 2\pi $ when $ t = \frac{\pi}{5} $. This is the fundamental period.
Here is an example of a non-periodic function:
$ e^{(-1+j)t} $
$ = e^{-t}(\cos t + j \sin t) $
This funtion is not periodic because the $ e^{-t} $ term makes the function decay exponentially.
