Question:medium

Let a point $P$ in the Argand plane represent the complex number $z$. If \[ \operatorname{Arg}\left(\frac{2z-i}{z-2}\right)=\frac{\pi}{4}, \] then the locus of $P$ is

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For locus problems involving $\operatorname{Arg}$, first write $z=x+iy$, simplify the complex expression, and then use the given argument condition to relate its real and imaginary parts.

Updated On: Jul 29, 2026

$4x^2-2xy+2y^2+6x-5y+2=0$
$2x^2+2y^2-3x+3y-2=0$
$x^2+2y^2-3x+2y-2=0$
$2x^2+xy+2y^2-3x-y-2=0$

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The Correct Option is B

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Let a point \(P\) in the Argand plane represent the complex number \(z\). If \[ \operatorname{Arg}\left(\frac{2z-i}{z-2}\right)=\frac{\pi}{4}, \] then the locus of \(P\) is

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The Correct Option is B

Solution and Explanation

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