The equation ( z-1 z+1 )= 4 represents a circle with: - Vidyadip

MCQ

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

A
centre at $(0,-1)$ and radius $\sqrt{2}$
✓
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

Correct option: B.

centre at $(0,1)$ and radius $\sqrt{2}$

b
In $\triangle \mathrm{OAC}$

$\sin \left(\frac{\pi}{4}\right)=\frac{1}{\mathrm{AC}}$

$\Rightarrow \mathrm{AC}=\sqrt{2}$

Also, $\tan \frac{\pi}{4}=\frac{\mathrm{OA}}{\mathrm{OC}}=\frac{1}{\mathrm{OC}}$

$\Rightarrow \mathrm{OC}=1$

$\therefore$ centre $(0,1) ;$ Radius $=\sqrt{2}$

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