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math college calculus

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

Apr 2nd, 2015

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

(–27)1/5 = 271/5 ({cos [π/5 + (2 /5)πk] + i sin [π/5 + (2 /5)πk]} where k = 0, 1, 2, 3, and 4

z1 = 271/5 [cos (π/5) + i sin (π/5)] = 1.56 + 1.14i

z2 = 271/5 [cos (3π/5) + i sin (3π/5)] =–0.597 + 1.84i

z3 = 271/5 [cos π + i sin π] = – 271/5 = – 1.93

z4 = 271/5 [cos (7π/5) + i sin (7π/5)] = – 0.597 – 1.84i

z5 = 271/5 [cos (9π/5) + i sin (9π/5)] = 1.56 – 1.14i

Apr 2nd, 2015

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