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Question

(cosθ+isinθ)4(sinθ+icosθ)5 is equal to


A

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B

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C

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D

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Solution

The correct option is D


(cosθ+isinθ)4(sinθ+icosθ)5= (cosθ+isinθ)4i5(1isinθ+cosθ)5

= (cosθ+isinθ)4i(cosθisinθ)5= (cosθ+isinθ)4i(cosθ+isinθ)5 (By Property)

= 1i(cosθ+isinθ)9=sin9θ-icos9θ.


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