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how to find the 5th root of -32 

Guest Mar 25, 2017
 #1
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(Odd number)-th root of a negative number is also a negative number.

\(\sqrt[5]{-32}\\ =-\sqrt[5]{32}\\ =-2\)

MaxWong  Mar 25, 2017
 #2
avatar+92781 
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Yes     \(\sqrt{-32}=-2\)

And that I think is the only answer BUT

 

if

\(x^5=-32\\ then\\ x=2cis(\pi+\frac{2\pi n}{5})\qquad n \in Z\\ x=2cis(\frac{5\pi}{5}+\frac{2\pi n}{5})\qquad n \in Z\\ x=2cis(\frac{\pi}{5}),\quad x=2cis(\frac{3\pi}{5}),\quad x=2cis(\frac{5\pi}{5}),\quad x=2cis(\frac{7\pi}{5}),\quad x=2cis(\frac{9\pi}{5})\\ x=2cis(\frac{\pi}{5}),\quad x=2cis(\frac{3\pi}{5}),\quad x=-2,\quad x=2cis(\frac{7\pi}{5}),\quad x=2cis(\frac{9\pi}{5})\\ \)

Melody  Mar 26, 2017

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