find all the complex fifth roots of −27 hint; z1/n= r1/n cos(θ+2πk/n )+i sin(θ+2πk/n )

–27 = 27(cos π + i sin π) has five fifth roots

(–27)^{1/5} = 27^{1/5 }({cos [π/5 + (2 /5)πk] + i sin [π/5 + (2 /5)πk]} where k = 0, 1, 2, 3, and 4

z_{1} = 27^{1/5 }[cos (π/5) + i sin (π/5)] = 1.56 + 1.14i

z_{2} = 27^{1/5 }[cos (3π/5) + i sin (3π/5)] =–0.597 + 1.84i

z_{3} = 27^{1/5 }[cos π + i sin π] = – 27^{1/5 }= – 1.93

z_{4} = 27^{1/5 }[cos (7π/5) + i sin (7π/5)] = – 0.597 – 1.84i

z_{5} = 27^{1/5 }[cos (9π/5) + i sin (9π/5)] = 1.56 – 1.14i

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