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°).