If the curve represented by the locus of a point in the Argand plane corresponding to the complex number \(z\) satisfying the relation
\[
\operatorname{Re}\!\left(\frac{z+4}{2z-5}\right)
+
\operatorname{Re}\!\left(\frac{\bar z+4}{2\bar z-5}\right)
=4
\]
cuts the \(X\)-axis at two points \(A\) and \(B\), then the sum of the abscissae of those two points is
Show Hint
For any complex number \(w\),
\[
\boxed{\operatorname{Re}(w)=\operatorname{Re}(\bar w).}
\]
Hence,
\[
\operatorname{Re}(w)+\operatorname{Re}(\bar w)
=
2\operatorname{Re}(w),
\]
which simplifies many locus problems.