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Question

(cosθ+isinθsinθ+icosθ)4 equals


A

sin8θ - icos8θ

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B

cos8θ + isin8θ

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C

sin8θ + icos8θ

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D

cos8θ + isin8θ

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Solution

The correct option is D

cos8θ + isin8θ


(cosθ+isinθsinθ+icosθ)4 =(cosθ+isinθ)4i4(cosθisinθ)4=cos4θ+isin4θcos4θisin4θ

=(cos4θ+isin4θ)(cos4θ+isin4θ)(cos4θisin4θ)(cos4θ+isin4θ)

=(cos4θ+isin4θ)2cos24θ+sin24θ=cos8θ + isin8θ


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