Question

state and prove De movre's theorem for a rational index.​

Answer 1

Answer:

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Demoivre's Theorem – Integral and Rational Indices. If n is a rational number, then one of the values of (cosθ + i sinθ)ⁿ is cos nθ + i sinnθ. (ii) (cosθ + i sinθ)⁻ⁿ = cos (-n)θ + i sin(-n)θ = cos nθ – i sinnθ provided 'n' is an integer. ... Provided 'n' is an integer.

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Answer 2

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Demoivre's Theorem – Integral and Rational Indices. If n is a rational number, then one of the values of (cosθ + i sinθ)ⁿ is cos nθ + i sinnθ. (ii) (cosθ + i sinθ)⁻ⁿ = cos (-n)θ + i sin(-n)θ = cos nθ – i sinnθ provided 'n' is an integer. ... Provided 'n' is an integer.