Question

Equation of tangent drawn to circle $| z |= r$, at the point $A \left( z _0\right)$, is $\frac{ z }{ z _0}+\frac{\overline{ z }}{\overline{ z }_0}= p$, find the value of $P$

Answer 1

$ \arg \cdot\left(\frac{ z _0- z }{0- z _0}\right)=\frac{\pi}{2} $
$\text { arg. }\left(\frac{ z - z _0}{ z _0}\right)=\frac{\pi}{2} \Rightarrow \frac{ z - z _0}{ z _0}= ik $
$\frac{ z - z _0}{ z _0}+\frac{\overline{ z }-\overline{ z }_0}{\overline{ z }_0}=0 $
$\frac{ z }{ z _0}+\frac{\overline{ z }}{\overline{ z }_0}=2 $