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19-05-2021
Mathematics

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Find the three cube roots of Z = -2 + 2i.

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nouni2001 nouni2001

19-05-2021

r = radical (-2)^2 + 2^2 = rad 8
Tan ø = 2/-2 = -1 so ø=45 degrees
But z is in the second quadrant so ø=135 deg
For k = 0, the first root is 1 + i
For k = 1, the second root is -1.366 + 0.366i
For k = 2, the third root is 0.366 - 1.366i

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