Q.

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

2

b

1

c

0

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+cosθ12=0sinθ+cosθ=2

θπ4,4,4,4

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