AP EAMCET · Maths · Complex Number
If a complex number \(z=x+i y\) represents a point \(P\) on the Argand plane and \(\operatorname{Arg}\left(\frac{z-3+2 i}{z+2-3 i}\right)=\frac{\pi}{4}\), then the locus of \(P\) is a
- A circle with the line \(\mathrm{x}+\mathrm{y}=12\) as its diameter
- B circle with radius \(\sqrt{11}\)
- C circle with the line \(x-y=6\) as its diameter
- D circle with radius 5
Answer & Solution
Correct Answer
(D) circle with radius 5
Step-by-step Solution
Detailed explanation
\(\operatorname{Arg}\left(\frac{z-(3-2i)}{z-(-2+3i)}\right)=\frac{\pi}{4}\) Let \(z=x+iy\). Then \(\frac{((x-3)+i(y+2))}{((x+2)+i(y-3))} = \frac{X_{num}+iY_{num}}{D}\).…
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