Mathematics - Complex Number Question with Solution | TestHub

Let $z=x+iy,$ then

$Im \left[\left(\frac{ix-y-2}{x+\left(y-1\right)i}\right) \left(\frac{x-\left(y-1\right)i}{x-\left(y-1\right)i}\right)\right]+1=\frac{\left(y-1\right) \left(y+2\right)+x^2}{x^2+{\left(y-1\right)}^2}+1=0$

$\Rightarrow 2x^2+2y^2-y-1=0$

$\Rightarrow x^2+y^2-\frac{y}{2}-\frac{1}{2}=0$

Center $(0, \frac{1}{4})$

Radius $=\sqrt{g^2+f^2-c}$

Radius$= \sqrt{\frac{1}{16}+\frac{1}{2}}= \sqrt{\frac{9}{16}}=\frac{3}{4}$