well ive figured it out for 4th root just treat it like (-4)^(1/4) as ((-4)^(1/2))^(1/2) then you get

2i^(1/2)

so you must find the number A + Bi such that it ^2 = 2i so just say

(A +Bi)^2 = 2i
(A + Bi)(A + Bi) = 2i
A^2 + ABi - B^2 = 2i

A^2 - B^2 must = 0 as there is no constant
so A^2 - B^2 = 0 and solve
A^2 = B^2 and so
A = B

so A^2 + A^2 i - A^2 = 2i
A^2 i = 2i
A^2 = 2
A = 2^(1/2)

and you get your answer but i cant seem to get it to work out for 6,8,10 ect.

any ideas??