SOLUTION: how can you show that √3+i/2 is a cube root of i

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Question 235867: how can you show that √3+i/2 is a cube root of i
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Argand plane where multiplication
is done by multiplying amplitudes and adding
angles of the rotating vectors
sqrt%283%29%2F2+%2B+i%2F2 = sqrt%28%28sqrt%283%29%2F2%29%5E2+%2B+%281%2F2%29%5E2%29 angle 30 degrees
sqrt%28%28sqrt%283%29%2F2%29%5E2+%2B+%281%2F2%29%5E2%29 angle 30 degrees = 1 angle 30 degrees
i+=+%28sqrt%283%29%2F2+%2B+i%2F2%29%5E3
i = 1 angle 90 degrees
1 angle 90 degrees = 1%5E3 angle 30+%2B+30+%2B+30degrees
1 angle 90 degrees = 1 angle 90 degrees
It is best to draw this. The advantage is that the exponent could
be any size and you just add angles and raise 1 number to a power