1. Using the same value I used in HW1.
$ e^{\frac{1}{4}j\pi*n} $
This function can be periodic or non-periodic depending on the sampling rate. It will be periodic for any multiple of $ \frac{1}{8} $ as calculated in HW1. Similarly, for any sampling rate not a multiple of $ \frac{1}{8} $, the function will not be periodic.
2. Also using the same value I used in HW1.
$ e^{\sqrt{3}j\pi*n} $
As we learned in class, any DT function x[n] can be written as:
$ x[n]=\sum{inf}{k=-inf}{d[n-k]} $
By taking multiple unit impulses we can make a non-periodic function periodic.
