Find the fourth roots of 81 (cos 320° + i sin 320°). Write the answer in trigonometric form.

Using the De Moivre's Theorem, let us work out for the fourth roots of 81 (cos 320° + i sin 320°).

zⁿ = rⁿ (cos nθ + i sin nθ)

z⁴ = 81 (cos 320° + i sin 320°)

z = ∜[81 (cos 320° + i sin 320°) ]

= ∜[3^4 (cos 4*80° + i sin 4*80°) ]

= 3 (cos 80° + i sin 80°)