SOLUTION: please help me solve the equation: {{{x=i^(1/3)}}} also could you explain how to solve it

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Question 184166: please help me solve the equation: x=i%5E%281%2F3%29 also could you explain how to solve it
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
please help me solve the equation: x=i%5E%281%2F3%29
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If you are studying DeMoivre's Theorem in a trig class,
i = (cos(90+360n) + i sin(90+360n) where n = 1,2,3....
So: i^(1/3) = cos[(1/3)(90+360n)] + isin[(1/3)(90+360n)]
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Letting n = 1,then 2,then3 will give you three cube roots of "i".
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If n=1 you get: i^(1/3) = cos(150) + isin(150)
If n=2 you get: i^(1/3) = cos(270) + isin(270)
If n=3 you get: i^(1/3) = cos(30) + isin(30)
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Cheers,
Stan H.