JEE MAIN - Mathematics (2021 - 26th August Morning Shift - No. 7)
The equation $$\arg \left( {{{z - 1} \over {z + 1}}} \right) = {\pi \over 4}$$ represents a circle with :
centre at (0, $$-$$1) and radius $$\sqrt 2 $$
centre at (0, 1) and radius $$\sqrt 2 $$
centre (0, 0) and radius $$\sqrt 2 $$
centre at (0, 1) and radius 2
Explanation
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In $$\Delta$$OAC
$$\sin \left( {{\pi \over 4}} \right) = {1 \over {AC}}$$
$$ \Rightarrow AC = \sqrt 2 $$
Also, $$\tan {\pi \over 4} = {{OA} \over {OC}} = {1 \over {OC}}$$
$$\Rightarrow$$ OC = 1
$$\therefore$$ centre (0, 1); Radius = $$\sqrt 2 $$
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