SOLUTION: Finding the Principal Root of a Complex Number (-8i)^(1/3)

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Question 1207569: Finding the Principal Root of a Complex Number
(-8i)^(1/3)
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


%28-8i%29%5E%281%2F3%29

Write the given complex number in cis(theta) form:

%288cis%28270%29%29%5E%281%2F3%29

Use deMoivre's Theorem to find the principal root:

%28%288%5E%281%2F3%29%29%28cis%28270%2F3%29%29%29=2cis%2890%29

Convert the result back to a+bi form:

2%280%2Bi%29=2i

ANSWER: 2i

CHECK:
%282i%29%5E3=8i%5E3=8%28-i%29=-8i