To prove: If ω = cos 2 π n + i sin 2 π n and u is any n th root of z ∈ ℂ , then the n th roots of z are given by ω u , ω 2 u , ⋯ , ω n − 1 u , ω n u = u .

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Answer 1

Question

Chapter 7.3, Problem 9E

To determine

To prove: If ω=cos 2πn+i sin 2πn and u is any n th root of z∈ℂ, then the n th roots of z are given by ωu, ω2u, ⋯, ωn−1u, ωnu=u.

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Answer 2

Question

Chapter 7.3, Problem 9E

To determine

To prove: If ω=cos 2πn+i sin 2πn and u is any n th root of z∈ℂ, then the n th roots of z are given by ωu, ω2u, ⋯, ωn−1u, ωnu=u.

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Answer 3

Question

Chapter 7.3, Problem 9E

To determine

To prove: If ω=cos 2πn+i sin 2πn and u is any n th root of z∈ℂ, then the n th roots of z are given by ωu, ω2u, ⋯, ωn−1u, ωnu=u.

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Answer 4

Question

Chapter 7.3, Problem 9E

To determine

To prove: If ω=cos 2πn+i sin 2πn and u is any n th root of z∈ℂ, then the n th roots of z are given by ωu, ω2u, ⋯, ωn−1u, ωnu=u.

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Answer 5

Chapter 7.3, Problem 9E

To determine

To prove: If ω=cos 2πn+i sin 2πn and u is any n th root of z∈ℂ, then the n th roots of z are given by ωu, ω2u, ⋯, ωn−1u, ωnu=u.

Answer 6

Chapter 7.3, Problem 9E

To determine

To prove: If ω=cos 2πn+i sin 2πn and u is any n th root of z∈ℂ, then the n th roots of z are given by ωu, ω2u, ⋯, ωn−1u, ωnu=u.

Answer 7

Chapter 7.3, Problem 9E

To determine

To prove: If ω=cos 2πn+i sin 2πn and u is any n th root of z∈ℂ, then the n th roots of z are given by ωu, ω2u, ⋯, ωn−1u, ωnu=u.

Answer 8

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Answer 9

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Answer 10

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Answer 11

To prove: If ω = cos 2 π n + i sin 2 π n and u is any n th root of z ∈ ℂ , then the n th roots of z are given by ω u , ω 2 u , ⋯ , ω n − 1 u , ω n u = u .

Solution Summary: The author explains De Moivre's Theorem: if n is a positive integer and z=r (mathrmcostheta +i

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To prove: If ω=cos 2πn+i sin 2πn and u is any n th root of z∈ℂ, then the n th roots of z are given by ωu, ω2u, ⋯, ωn−1u, ωnu=u.

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Chapter 7 Solutions