Question

The mirror image of the curve $arg\left(\frac{z-3}{z-i}\right)=\frac{\pi }{6},i=\sqrt{-1}$ in the real axis is ___________________.

• A. $arg\left(\frac{z+3}{z+i}\right)=\frac{\pi }{6}$
• B. $arg\left(\frac{z-3}{z+i}\right)=\frac{\pi }{6}$
• C. $arg\left(\frac{z+i}{z+3}\right)=\frac{\pi }{6}$
• D. $arg\left(\frac{z+i}{z-3}\right)=\frac{\pi }{6}$

Answer 1

The correct option is D $arg\left(\frac{z+i}{z-3}\right)=\frac{\pi }{6}$

The image of $z$ in the real axis is $\overline{z}$

$\therefore$ image is given by

$\arg \left(\frac{\overline{z}-3}{\overline{z}-i}\right)=\frac{\pi }{6}$

$\Rightarrow -arg\left(\frac{z-3}{z+i}\right)=\frac{\pi }{6}$

$\Rightarrow arg\left(\frac{z+i}{z-3}\right)=\frac{\pi }{6}$