Question

Which of the following is a third root of the given complex number? 27(cos(pi/5)+isin(pi/5))

Answer 1

The third root of the given complex number 27(cos(pi/5)+isin(pi/5)) is 3(cos(pi/15)+i sin(pi/15)) 

The solution would be like this for this specific problem:   2^5 = 32 so you need a 2 out front the 5th root of cos(x) + i sin(x) is cos(x/5) + i sin(x/5). Additionally, 5 roots are located at even intervals around the circle. They are spaced every 2 pi/5 or 6 pi/15 radians.   Roots are located at pi/15, pi/15+ 10pi/15 = 11 pi/15 and pi/15+ 20pi/15 = 21 pi/15 (or 7 pi /5 ).