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
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a
1
b
0
c
2
d
4
answer is D.
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Detailed Solution
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