Q.
If z≠1, z2z-1 is real, then point represented by the complex number z lies
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a
on circle with centre at the origin.
b
either on the real axis or on a circle not passing through the origin.
c
on the imaginary axis.
d
either on the real axis or on a circle passing through the origin
answer is B.
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Detailed Solution
As z2z-1 is real, we get z2z−1=z¯2z¯−1⇔z2(z¯−1)=z¯2(z−1)⇔zz¯(z−z¯)−(z−z¯)(z+z¯)=0⇔(z−z¯)(zz¯−z−z¯)=0⇒z−z¯=0 or zz¯−z−z¯=0⇒ z lies on the real axis or z lies on a circle through the origin.
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