SOLUTION: Find the 3 complex solutions to the equation z^3 + 2i = 0

Question 385329: Find the 3 complex solutions to the equation z^3 + 2i = 0
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the 3 complex solutions to the equation z^3 + 2i = 0
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z^3 = -2i
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Since i^2 = -1
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z^3 = 2i^3
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z^3-(cbrt(2)i)^3 = 0
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Factor:
(z-(cbrt(2)i)(z^2+(cbrt(2)i)+(cbrt(2)i)^2)=0
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z = cbrt(2)i plus two solution from the quadratic factor.
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I'll leave the quadratic to you.
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You could also work this problem by converting to polar form.
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Cheers,
Stan H.
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