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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