[JEE Main 2012] if z 1 and z 2 z 1 is real then the point z
If $z\ne1$ and $\dfrac{z^2}{z-1}$ is real, then the point $z$ lies
(a) either on the real axis or on a circle through the origin
(b) on a circle with centre at the origin
(c) either on the real axis or on a circle not through the origin
(d) on the imaginary axis
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (a) either on the real axis or on a circle through the origin
Setting $\operatorname{Im}\frac{z^2}{z-1}=0$ factors as $y\,(x^2+y^2-x)=0$: either $y=0$ (real axis) or $x^2+y^2-x=0$ (a circle through the origin).
JEE Main 2012 · Complex Numbers — verified solution by the Vidaara Team.
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