Find the complex cube roots of 216cos120 degree epsilon 120

Find the complex cube roots of 216(cos120 degree +epsilon 120 degree). Leave your answers in trigonometric form with the argument in degrees. 0 lessthanorequalto 6

Solution

z = 216*[cos120 + i*sin120]

Using De-Moivre\'s Theorwm

z^1/3 = 216^1/3*[cos120/3 + i*sin120/3]

z^1/3 = 6*[cos40 + i*sin40]