Question

If $k+\left|k+z^2\right|={\left|z\right|}^2\left(k\in R^{-}\right),$ then possible argument of $z$ is

• A. $0$
• B. $\pi$
• C. $\pi /2$
• D. none of these

Answer 1

Answer: (C)

$|k+z^2|=|z^2|-k=|z^2|+|k|$
$\Rightarrow k,z^2$ and $0+i0$ are collinear
$\Rightarrow$ arg $(z^2)=$ arg $(k)$
$\Rightarrow 2$ arg $(z)=\pi$
$\Rightarrow$ arg $(z)=\frac{\pi }{2}$