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

Question

The equation $\arg\!\left(\dfrac{z-1}{z+1}\right)=\dfrac\pi4$ represents a circle with

Accepted Answer

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 = $$\sqrt 2 $$

Solutions · 1