TS EAMCET · Maths · Complex Number
Let \(z=x+\) iy be a point in the Argand plane. If the amplitude of \(\left(\frac{z-3}{z+2 i}\right)\) is \(\frac{\pi}{2}\), then the locus of \(\mathrm{z}\) is
- A a circle
- B a straight line
- C a semicircular arc not containing the origin
- D a semicircular are containing the origin
Answer & Solution
Correct Answer
(D) a semicircular are containing the origin
Step-by-step Solution
Detailed explanation
\(\operatorname{Amp}\left(\frac{Z-3}{Z+2 i}\right)=\operatorname{Amp}(Z-3)-\operatorname{Amp}(Z+2 i)=\frac{\pi}{2}\) if \(\operatorname{Amp}\left(\frac{Z-Z_1}{Z-Z_2}\right)=\frac{\pi}{2}\) \(\Rightarrow\) Locus of \(Z\) is an arc as semicircle. Putting \(Z=0\)…
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