Question

The region of the complex plane for which $\left|\frac{z-a}{z+\overline{a}}\right|=1$ where $\mathrm{Re}\left(a\right)\ne 0$ is

• A. $x-axis$
• B. $y-axis$
• C. The straight line $x=a$
• D. None of these

Answer 1

The correct option is A $x-axis$

$\begin{array}{c}\left|\frac{z-a}{z-\overline{a}}\right|=1\\ \left|z-a\right|=\left|z-\overrightarrow{a}\right|\\ whichliesaperpendicularbi\sec torof\overline{a}\&a\\ \Rightarrow x-axis\\ hence,theoptionAisthecorrectanswer.\end{array}$