Question 325079
(-16)^1/4 how do I evaluate this expression
= {{{(1/16)^(1/4)}}}
= {{{sqrt(sqrt(-16))}}}
= {{{sqrt(4i)}}} and {{{sqrt(-4i)}}}
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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.