Calculate the sets of
(a) the third roots of $-8$, and (b) the fourth roots of $-i$.
The problem is we did not get any definition we can rely on, no number sets given, just the text above, but I think we should do it for the real numbers. How would you do that, on which definition would you rely on? We did nothing regarding roots.
If your third roots of $-8$ is $re^{i\theta } $, then $$r^3 e^{3i\theta} = -8 = 8 e^{i\pi}$$
You need to solve for r and all possible solutions of $\theta$ which give you three distinct roots of $-8$
Similarly for the fourth roots of $-i$, you want $$r^4 e^{4i\theta}= -i = e^{3i\pi/2}$$