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Question

Let z be a complex number having the argument θ,0<θ<π/2 and satisfying the equality |z3i|=3. Then cotθ6z is equal to

A
i
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B
i
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C
2i
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D
1
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Solution

The correct option is B i
let, z=r(cosθ+isinθ). Now,
r=OAsinθ=6sinθ
z=6sinθ(cosθ+isinθ)
or 6z=1sinθ(cosθ+isinθ)
=cosθisinθsinθ
=i+cotθ
or cotθ6z=i
Ans: B

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