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Q.

If (1+cosθ+isinθ) (1+cos2θ+isin2θ)=x+iy  then y =

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a

xtan(3θ2)

b

xtan(5θ2)

c

xtan(7θ2)

d

xtan(9θ2)

answer is A.

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Detailed Solution

(1+cosθ+isinθ)(1+cos2θ+isin2θ) =2cosθ2[cosθ2+sinθ2]2cosθ[cosθ+isinθ] =2cosθ2.cosθ[cisθ2](cisθ) =4.cosθ2.cosθ(cos3θ2+isinθ2) Comparing with x + iyx=4cosθ2cosθcos3θ2 y=4cosθ2cosθsin3θ2 ∴xy=cot3θ2 ⇒y=xtan3θ2
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