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Question

θ ∈ [0, 2π] and z1,z2,z3 are three complex numbers such that they are collinear and

(1+|sinθ|)z1 + (|cosθ|1)z2 - 2z3 =0. If at least one of the complex numbers z1,z2,z3 is

non-zero then number of possible values of θ is


A

Infinite

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B

4

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C

2

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D

8

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Solution

The correct option is B

4


If z1,z2,z3 are collinear and az1+bz2+cz3 = 0 then a + b + c = 0. Hence

1 + |sinθ| + |cosθ| - 1 - 2 = 0 |sinθ| + |cosθ| = 2

θ = π4, 3π4, 5π4, 7π4


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