Question

If Arg $(z+i)-$ Arg $(z-i)$ $=\frac{\pi }{2}$, then $z$ lies on a ..........

• A. Circle
• B. Line
• C. Coordinate axes
• D. None of these

Answer 1

The correct option is A Circle

Putting z = x+iy,

${tan}^{-1}\frac{y+1}{x}$ - ${tan}^{-1}\frac{y-1}{x}$ = $\pi$/2

$\Rightarrow$ 1 + ($\frac{y+1}{x})$($\frac{y-1}{x}$) = 0

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

It is a circle of center coinciding with origin and radius 1 units.

Hence, option A is correct.