If the set \(\left{\mathrm{Re}\left(\frac{z−\overset{¯}{z}+z\overset{¯}{z}}{2−3z+5\overset{¯}{z}}\right):z\in C,\mathrm{…

If the set \(\left{\mathrm{Re}\left(\frac{z−\overset{¯}{z}+z\overset{¯}{z}}{2−3z+5\overset{¯}{z}}\right):z\in C,\mathrm{Re}(z)=3\right}\) is equal to the interval \((\alpha ,\beta ]\), then 24 \((\beta −\alpha )\) is equal to

[JEE Main 2023, 15 Apr (Shift 1)]