To simplify the expression \( (7 - \sqrt{-64}) + (6 + 3i) \), we first need to simplify \( \sqrt{-64} \).
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Simplify \( \sqrt{-64} \): \[ \sqrt{-64} = \sqrt{64} \cdot \sqrt{-1} = 8i \]
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Replace \( \sqrt{-64} \) in the original expression: \[ (7 - \sqrt{-64}) + (6 + 3i) = (7 - 8i) + (6 + 3i) \]
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Combine like terms:
- Combine the real parts: \( 7 + 6 = 13 \)
- Combine the imaginary parts: \( -8i + 3i = -5i \)
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Write the final result: \[ 13 - 5i \]
Thus, the simplified expression is: \[ \boxed{13 - 5i} \]