How to find the 4th root of a complex number !!

Question

What are the fourth roots of 6+6√(3i) ?

Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure.

 

(  )cis(  )

(  )cis(  )

(  )cis(  )

(  )cis(  )

 

Hello! I really need help on this. I tried looking up videos on how to do this, but I'm really confused.. If someone could help me, I'd appreciate that a lot.

Thank you so much.

:)

Answer 1

z = 6 + 6i

|| z || = 12

θ = 60º

12^1/4 (cos 60º / 4 + i sin 60º / 4)

12^1/4 (cos 420º / 4 + i sin 420º / 4)

12^1/4 (cos 780º / 4 + i sin 780º / 4)

12^1/4 (cos 1140º / 4 + i sin 1140º / 4)

Answer 2