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Question

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 ____________.

Correct Answer
14

Solution

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