Find all the complex roots Leave your answer in polar form w

Find all the complex roots. Leave your answer in polar form with The complex cube roots of 6 + 6 Squareroot 3i z_0 = (cos + i sin) (Simplify your answer, including any radicals. Type an exact answer)

Solution

6+6sqrt3 i

r=sqrt(36+108)=12

Theta=tan^-1(6sqrt3/6) =tan^-1(sqrt3)=pi/3

(12(cos(pi/3)+isin(pi/3)))^1/2 = 12^1/2(cos(pi/6) +i sin(pi/6))

2sqrt3(cos(pi/6)+i sin(pi/6))