If the amplitude of $(Z-2)$ is $\frac{\pi}{2}$ then the locus of $Z$ is

If the amplitude of $(Z-2)$ is $\frac{\pi}{2}$ then the locus of $Z$ is
  1. $x=0, y\gt0$
  2. $x=2, y\gt0$
  3. $x\gt0, y=2$
  4. $x\gt0, y=0$

Solution

$\begin{aligned} & \text { } Z=x+\mathrm{i} y \\ & Z-2=x-2+i y \\ & \arg (Z-2)=\frac{y}{x-2}=\infty \Rightarrow x=2 ; y\gt0\end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 1)

Practice more Complex Number questions on Aicharya