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

Answer: 2

$\arg \cdot \left(\frac{z_0-z}{0-z_0}\right)=\frac{\pi }{2}$
$\text{ arg. }\left(\frac{z-z_0}{z_0}\right)=\frac{\pi }{2}\Rightarrow \frac{z-z_0}{z_0}=ik$
$\frac{z-z_0}{z_0}+\frac{\overline{z}-{\overline{z}}_0}{{\overline{z}}_0}=0$
$\frac{z}{z_0}+\frac{\overline{z}}{{\overline{z}}_0}=2$