Question

Let $OP.OQ=1$ and let $O,P,Q$ be three collinear points. If $O$ and $P$ represents the complex numbers $0$ and $z$ then $P$ represents

• A. $\frac{1}{z}$
• B. $\overline{z}$
• C. $\frac{1}{\overline{z}}$
• D. none of these

Answer 1

Answer: (C)

$\frac{1}{\overline{z}}$

Let
$O=0+0i$

$P=z$

$Q=z_1$

Now

$OP=z$

$OQ=z_1$

$OP.OQ=1$

$z.z_1=1$

$z_1=\frac{1}{z}$

$z_1=\overline{z}$

Therefore

$O=0$

$P=z=(\frac{1}{z}{)}^{-1}=\frac{1}{\overline{z}}$

$Q=\overline{z}$

Hence, option 'C' is correct.