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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

  1. A circle with the line \(\mathrm{x}+\mathrm{y}=12\) as its diameter
  2. B circle with radius \(\sqrt{11}\)
  3. C circle with the line \(x-y=6\) as its diameter
  4. D circle with radius 5
Verified Solution

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 \(\frac{((x-3)+i(y+2))}{((x+2)+i(y-3))} = \frac{X_{num}+iY_{num}}{D}\).…