Question:
The equation $\arg \left(\frac{\mathrm{z}-1}{\mathrm{z}+1}\right)=\frac{\pi}{4}$ represents a circle with:
Correct Option: 2,
Solution:
In $\Delta \mathrm{OAC}$
$\sin \left(\frac{\pi}{4}\right)=\frac{1}{\mathrm{AC}}$
$\Rightarrow \mathrm{AC}=\sqrt{2}$
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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