SOLUTION: (-16)^1/4 how do I evaluate this expression

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Question 325079: (-16)^1/4 how do I evaluate this expression
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(-16)^1/4 how do I evaluate this expression
= %281%2F16%29%5E%281%2F4%29
= sqrt%28sqrt%28-16%29%29
= sqrt%284i%29 and sqrt%28-4i%29
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A better method:
-16 = 16cis(180 + n*360)
(16cis(180+n*360))^(1/4) = 2cis(45+n*90)
= 2cos(45) + 2i*sin(45) = sqrt(2) + i*sqrt(2)
= 2cos(135) + 2i*sin(135) = -sqrt(2) + i*sqrt(2)
= 2cos(225) + 2i*sin(225) = -sqrt(2) - i*sqrt(2)
= 2cos(315) + 2i*sin(315) = +sqrt(2) - i*sqrt(2)
4th root, 4 answers above.