SOLUTION: How do you find all the solutions (complex numbers included) of {{{x^5-32=0}}}?

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Question 1206992: How do you find all the solutions (complex numbers included) of x%5E5-32=0?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Use deMoivre's Theorem.

x%5E5-32=0
x%5E5=32

ANSWERS:
(1) x%5E5=32=32cis%280%29=32e%5E%280i%29; x=%28x%5E5%29%5E%281%2F5%29=2cis%280%29=2e%5E%28i%280%29%29=2
(2) x%5E5=32=32cis%282pi%29=32e%5E%28%282pi%29i%29; x=%28x%5E5%29%5E%281%2F5%29=2cis%28%282pi%29%2F5%29=2e%5Ei%282pi%2F5%29
(3) x%5E5=32=32cis%284pi%29=32e%5E%28%284pi%29i%29; x=%28x%5E5%29%5E%281%2F5%29=2cis%28%284pi%29%2F5%29=2e%5Ei%284pi%2F5%29
(4) x%5E5=32=32cis%286pi%29=32e%5E%28%286pi%29i%29; x=%28x%5E5%29%5E%281%2F5%29=2cis%28%286pi%29%2F5%29=2e%5Ei%286pi%2F5%29
(5) x%5E5=32=32cis%288pi%29=32e%5E%28%288pi%29i%29; x=%28x%5E5%29%5E%281%2F5%29=2cis%28%288pi%29%2F5%29=2e%5Ei%288pi%2F5%29