Question

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

Answer 1

Answer: 3(cos(11pi/15)+isin(11pi/15)) and 3(cos(pi/15)+isin(pi/15))

Step-by-step explanation: ap3x yw

Answer 2

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 ).