SOLUTION: How to find three cube roots of -64i?

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Question 1074318: How to find three cube roots of -64i?
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!


Therefore:



We use DeMoivre's theorem to multiply the angle by the exponent 1%2F3:






We can use any three consecutive integers for n to obtain the
three cube roots:

Using n=0



Using n=1



Using n=2



So the three cube roots of -64i are

4i, -2sqrt%283%29-2i, and 2sqrt%283%29-2i

Edwin