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Question

If θ=π2 then the 10th term of the series
1+(cosθ+isinθ)+(cosθ+isinθ)2+....is

A
i
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B
1
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C
1
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D
i
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Solution

The correct option is A i
1+(cosθ+isinθ)+(cosθ+isinθ)2....
So the tenth term = (cosθ+isinθ)9
Using de Moivre's theorm = eiθ9
Putting θ=x2 , we get
ei9x2
=eix2
=cosx2+isinx2
=i

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