Questions
If is real, then point represented by the complex number lies
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
detailed solution
Correct option is B
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.Talk to our academic expert!
Similar Questions
If and then implies, that, in the complex plane
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