TS EAMCET · Maths · Complex Number
If the amplitude of \(z-2-3 i\) is \(\pi / 4\), then the locus of \(z=x+i y\) is
- A \(x+y-1=0\)
- B \(x-y-1=0\)
- C \(x+y+1=0\)
- D \(x-y+1=0\)
Answer & Solution
Correct Answer
(D) \(x-y+1=0\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, } \arg (z-2-3 i)=\frac{\pi}{4} \Rightarrow z=x+i y \\ & z-2-3 i=x+i y-2-3 i=(x-2)+(y-3) i \\ & \arg (z-2-3 i)=\tan ^{-1}\left(\frac{y-3}{x-2}\right)=\frac{\pi}{4} \Rightarrow \frac{y-3}{x-2}=\tan \frac{\pi}{4} \\ & \quad y-3=x-2 \Rightarrow…
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