If z1 and z2 are two distinct points in an argand plane such that a|z1|=b|z2| (where a,b∈R), then the point (az1bz2+bz2az1) will always lie on the
A
line segment [−2,2] of the real axis
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B
line segment [−2,2] of the imaginary axis
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C
unit circle |z|=1
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D
the line whose arg(z)=tan−12
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Solution
The correct option is A line segment [−2,2] of the real axis Assuming arg(z1)=θ and arg(z2)=θ+α, az1bz2+bz2az1=a|z1|eiθb|z2|ei(θ+α)+b|z2|ei(θ+α)a|z1|eiθ =e−iα+eiα=2cosα Hence, the point will always lie on the line segment [−2,2] of the real axis.