If | z | = 1 and z 1 , then all the values of z 1 - z 2 lie on [2007]

Question

If $| z |$ $= 1$ and $z \neq \pm 1$ , then all the values of $\frac{z}{1 - z^{2}}$ lie on [2007]

Smart Achievers · Accepted Answer

(4)

$Given: | z | = 1 and z \neq \pm 1$

$To find the locus of ω = \frac{z}{1 - z^{2}}$

$Now, ω = \frac{z}{1 - z^{2}} = \frac{z}{z \bar{z} - z^{2}}$ $[∵ | z | = 1 \Rightarrow | z |^{2} = z \bar{z} = 1]$

$= \frac{1}{\bar{z} - z} = purely imaginary number$

$∴$ $ω must lie on y-axis.$

Want Us to Email you About Special Offers & Updates?