SOLUTION: Find the 3 cube roots of -i in polar form

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Question 1032727: Find the 3 cube roots of -i in polar form
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3+=+-i+=+cos%283%2Api%2F2+%2B+2k%2Api%29+%2B+i+sin%283%2Api%2F2+%2B2k%2Api%29
==> for k = 0, 1, 2, 3, 4,...
Choose k = 0, 1, and 2 to find the three distinct cube roots, and apply de Moivre's theorem

==> x+=+cos%28pi%2F2+%2B+2k%2Api%2F3%29+%2B++isin%28pi%2F2+%2B2k%2Api%2F3%29.
==> x%5B1%5D+=+cos%28pi%2F2%29+%2B++isin%28pi%2F2%29+=+i,
x%5B2%5D+=+cos%287pi%2F6%29+%2B++isin%287pi%2F6%29+=+-sqrt%283%29%2F2+-+i%2F2, and
x%5B3%5D+=+cos%2811pi%2F6%29+%2B++isin%2811pi%2F2%29+=+sqrt%283%29%2F2+-+i%2F2.