AP EAMCET · Maths · Complex Number
If the amplitude of \((Z-2)\) is \(\frac{\pi}{2}\) then the locus of \(Z\) is
- A \(x=0, y\gt0\)
- B \(x=2, y\gt0\)
- C \(x\gt0, y=2\)
- D \(x\gt0, y=0\)
Answer & Solution
Correct Answer
(B) \(x=2, y\gt0\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } Z=x+\mathrm{i} y \\ & Z-2=x-2+i y \\ & \arg (Z-2)=\frac{y}{x-2}=\infty \Rightarrow x=2 ; y\gt0\end{aligned}\)
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