What are the five fifth roots of -1?

Answer 1

Answer: -1

-0.309 ± j0.951

0.809 ± j0.588

Answer: This can easily be solved in polar coordinates.

-1 is 1, at an angle of 180 degrees. The fifth root of that is 1, at an angle of 180/5, or 36 degrees. To get additional roots, add (360/5) = 72 degrees at a time, to the angle. Use your scientific calculator's function to convert polar to rectangular, if you want to separate the real and the imaginary parts.