TS EAMCET · Maths · Complex Number
The point \(P\) denotes the complex number \(z=x+i y\) in the Argand plane. If \(\frac{2 z-i}{z-2}\) is a purely real number, then the equation of the locus of \(P\) is
- A \(2 x^2+2 y^2-4 x-y=0\)
- B \(x+4 y-2=0\) and \((x, y) \neq(2,0)\)
- C \(x-4 y-2=0\) and \((x, y) \neq(2,0)\)
- D \(x^2+y^2-4 x-2 y=0\)
Answer & Solution
Correct Answer
(B) \(x+4 y-2=0\) and \((x, y) \neq(2,0)\)
Step-by-step Solution
Detailed explanation
\(\frac{2 z-i}{z-2}=\frac{(2 x+2 i y-i)}{x+i y-2}=\frac{2 x+i(2 y-1)}{(x-2)+i y}\) For \((x, y)=(z, 0)\). This is not defined.…
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