Complex Numbers

Let \(\alpha = 8 - 14i,A = \left\{ {z \in c:{{\alpha z - \overline \alpha \overline z } \over {{z^2} - {{\left( {\overline z } \right)}^2} - 112i}}=1} \right\}\) and \(B = \left\{ {z \in c:\left| {z + 3i} \right| = 4} \right\}\). Then \(\sum\limits_{z \in A \cap B} {({\mathop{\rm Re}\nolimits} z - {\mathop{\rm Im}\nolimits} z)}\) is equal to ____________.