If x^4=y what does (x*i)^4 equal?

That should give you a big clue.

A similar trick works for any other kind of root, though it is only quite this easy for fourth roots. Once you've understood this one try it for cube roots noting that the cube roots of 1 are 1,w,w^2 where w=-0.5 + sqrt(-0.75) (or its square).