TS EAMCET · Maths · Complex Number
If the amplitude of \(z-2-3 i\) is \(\frac{\pi}{4}\), 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
We have, \(z-2-3 i=x+i y-2-3 i\) \(=(x-2)+i(y-3)\) Given, \(\tan ^{-1}\left(\frac{y-3}{x-2}\right)=\frac{\pi}{4} \Rightarrow y-3=x-2\) \(\therefore \quad x-y+1=0\)
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