Question

The equation $\arg \left(\frac{z-1}{z+1}\right)=\frac{\pi}{4}$ represents a circle with:

• A. centre at $(0,-1)$ and radius $\sqrt{2}$
• B. centre at $(0,1)$ and radius $\sqrt{2}$
• C. centre at $(0,0)$ and radius $\sqrt{2}$
• D. centre at $(0,1)$ and radius 2

Answer 1

Answer: (B)

In $\Delta OAC$
$\sin \left(\frac{\pi}{4}\right)=\frac{1}{ AC }$
$\Rightarrow AC =\sqrt{2}$
Also, $\tan \frac{\pi}{4}=\frac{ OA }{ OC }=\frac{1}{ OC }$
$\Rightarrow OC =1$
$\therefore $ centre $(0,1) ;$
Radius $=\sqrt{2}$