Complex Locus Circle (Jee Mains)

Geometry and Locus of Complex Numbers

Medium

Complex Locus Circle

If the locus of z ∈ C, such that
$\operatorname{Re} \left( {\frac{{z - 1}}{{2z + i}}} \right) + \operatorname{Re} \left( {\frac{{\bar z - 1}}{{2\bar z - i}}} \right) = 2$ ,
is a circle of radius r and center (a, b) then $\frac{{15ab}}{{{r^2}}}$ is equal to :

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