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 $=\sqrt{2}$