The cube roots can be found easily by converting the complex number into polar form.
z = -125i
z = 125<270, where angle is in degrees.
z^(1/3) = 125<((270 + k(360))/3)
= 125<(90 + 120k)
For k = 0:
z^(1/3) = 125<90 = 125i
For k = 1:
z^(1/3) = 125<210 = 125(-sqrt(3)/2 - i/2) = -125sqrt(3)/2 - 125/2*i
For k = 2:
z^(1/3) = 125<330 = 125(sqrt(3)/2 - i/2) = 125sqrt(3)/2 - 125/2*i
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