Question

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

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

Answer 1

The correct option is B centre at $(0,1)$ and radius $\sqrt{2}$

Here $OC=OA=1$


$\therefore$ Centre of circle $=(0,1)$
and radius of circle $=\sqrt{1^2+1^2}=\sqrt{2}$