Question

If $P,P^{\prime }$ represent the complex number $z_1$ and its additive inverse respectively, then the complex equation of the circle with $P{P}^{\prime }$ as a diameter is

• A. $\frac{z}{z_1}=\left(\frac{{\bar{z}}_1}{z}\right)$
• B. $z\bar{z}+z_1{\bar{z}}_1=0$
• C. $z\overline{z_1}+\bar{z}{z}_1=0$
• D. none of these

Answer 1

Answer: (A)

Clearly $\left|z\right|=\left|z_1\right|$
$\Rightarrow {\left|z\right|}^2={\left|z_1\right|}^2$



$\Rightarrow z\bar{z}=z_1{\bar{z}}_1$
$\Rightarrow \frac{z}{z_1}=\frac{{\overline{z}}_1}{\bar{z}}=\left(\frac{\overline{z}}{z}\right)$