Let \( S=z \in C:|z-3| \leq 1 \) and \( z(4+3 i)+\bar{z}(4-3 i) \leq 24 \). If \( \alpha+i \beta...

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Let \( S=z \in C:|z-3| \leq 1 \) and \( z(4+3 i)+\bar{z}(4-3 i) \leq 24 \).
If \( \alpha+i \beta \) is the point in \( S \) which is closest to \( 4 i \), then 25 \( (\alpha+\beta) \) is equal to
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