#1**0 **

(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**0 **

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