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Fourth roots of 81(cos320°+isin320°)

User Muthukumar
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Answer:

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°)

User Reinier
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