SOLUTION: FInd the cube roots of -8i (Answers may be left in trigonometric form). Having trouble solving this

Question 850587: FInd the cube roots of -8i (Answers may be left in trigonometric form). Having trouble solving this
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
FInd the cube roots of -8i (Answers may be left in trigonometric form).
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0-8i
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r = sqrt(0^2+8^2) = 8
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theta = arctan(-8/0) = (3/2)pi
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(-8i)^(1/3) = r(cis((3/2)pi + npi)/3
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Let n = 0 : (-8i)^(1/3) = 8cis(pi/2)
Let n = 1 : (-8i)^(1/3) = 8cis((3/2)+(1/3))pi) = 8cis((11/6)pi)
Let n = 2 : (-8i)^(1/3) = 8cis[(3/2) + (2/3)]pi= 8cis[(13/6)pi]
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Cheers,
Stan H.
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