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Q.

If x+iy=11−cos⁡θ+2isin⁡θ,θ≠2nπ,n∈I then  maximum value of x is

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a

1

b

2

c

12

d

13

answer is C.

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Detailed Solution

2x=(x+iy)+(x−iy)=2(1−cos⁡θ)(1−cos⁡θ)2+4sin2⁡θ⇒ x=15+3cos⁡θThus, maximum value of x is 12. It is attained at θ =π.
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