The trigonometric form of the complex number "-i" is cos(270°) + i*sin(270°).
The modulus of "-i" is 1, the argument is 270° = .
According to the general theory, there are three complex cube roots of "-i". They have the modulus of = 1.
The first cube root has the argument of 90° = , one third of the argument of "-i".
Each next cube root has the argument in = 120° = more than the previous one.
Thus the tree complex roots are
1) cos(90°) + i*sin(90°) = cis(90°) = i;
2) cos(90°+120°) + i*sin(90° + 120°) = cos(210°) + i*sin(210°);
3) cos(90°+240°) + i*sin(90° + 240°) = cos(330°) + i*sin(330°).