imaginary numbers

I dont know the first one but the second one is just -i

-i is correct though it would be better if you understood why.

\(\forall n \in \mathbb{Z} \\ i^{4n} = 1 \\ i^{4n+1}=i \\ i^{4n+2}=-1 \\ i^{4n+3}=-i\)

for the first problem we have

\(2\sqrt{-27} = 2\sqrt{27}\sqrt{-1} = 6\sqrt3 i = 6i \sqrt{3}\)

the 3rd choice