[JEE Advanced 2007] if z 1 and z 1 then all values of z 1 z 2
If $|z|=1$ and $z\ne\pm1$, then all values of $\dfrac{z}{1-z^2}$ lie on
(a) a line not through the origin
(b) $|z|=\sqrt2$
(c) the $x$-axis
(d) the $y$-axis
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
▲ 0
Correct answer: (d) the $y$-axis
$\frac{z}{1-z^2}=\frac1{\bar z-z}=\frac1{-2i\operatorname{Im}z}=\frac{i}{2\operatorname{Im}z}$, which is purely imaginary — the $y$-axis.
JEE Advanced 2007 · Complex Numbers — verified solution by the Vidaara Team.
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