Question

For a complex number $Z$ , the equation of the line of common chord of the circles $\left|Z-3\right|=2$ and $\left|Z\right|=2$ is

• A. $Z+\bar{Z}=3$
• B. $Z-\bar{Z}=3$
• C. $\bar{Z}-Z=3$
• D. $Z+\bar{Z}+3=0$

Answer 1

Answer: (A)

$\left|Z-3\right|=2\Rightarrow \left(Z-3\right)\left(\bar{Z}-\bar{3}\right)=4$
$\Rightarrow Z\bar{Z}-3Z-3\bar{Z}+9=\mathrm{4...},\left(1\right)$
$\left|Z\right|=2\Rightarrow Z\bar{Z}=\mathrm{4....}\left(2\right)$
For the equation of common chord, Subtracting $\left(2\right)$ from $\left(1\right)$ , we get,
$-3Z-3\bar{Z}+9=0$
$\Rightarrow Z+\bar{Z}=3$