Question

If '$z$' lies on the circle $|z-2i|=2\sqrt{2}$, then the value of $\arg \left[\frac{(z-2)}{(z+2)}\right]$ is equal to

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is B $\frac{\pi }{4}$



$CA=CB=2\sqrt{2},OC=2$
$\Rightarrow OA=OB=2$
$\Rightarrow A=2+0i,B=-2+0i$
Clearly, $\angle BCA=\frac{\pi }{2}$
$\Rightarrow P$ lies on the circumference of the circle
$\Rightarrow \angle BPA=\frac{\pi }{4}\text{or}\frac{3\pi }{4}$
$\Rightarrow \arg \left(\frac{z-2}{z+2}\right)=\frac{\pi }{4}$