Question

If $P, P'$ represent the complex number $z_1$ and its additive inverse respectively, then the complex equation of the circle with $PP'$ 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\bar {z_1} + \bar {z} z _1=0 $
• D. none of these

Answer 1

Answer: (A)

Clearly $\left|z\right|=\left|z_{1}\right|$
$\Rightarrow \left|z\right|^{2}=\left|z_{1}\right|^{2}$



$\Rightarrow z\,\bar{z}=z_{1}\,\bar{z}_{1}$
$\Rightarrow \frac{z}{z_{1}}=\frac{\overline{z}_{1}}{\bar{z}}=\left(\frac{\overline{z}}{z}\right)$