The given equation is $w^4 = 16j$. Rewriting the right side into polar form we get $16j = 16 e^{j\frac{\pi}{2}}$.
By comparing, we can see that $w = 2e^{j\frac{\pi}{8}+k\frac{\pi}{2}}$ where k is an integer.
So the possible values of w are: $2 e^{j\frac{\pi}{8}}$ $2 e^{j\frac{5\pi}{8}}$ $2 e^{j\frac{9\pi}{8}}$ $2 e^{j\frac{13\pi}{8}}$
From the given options, $2 e^{j\frac{2\pi}{8}}$ cannot be a value of $w$._
