Use the properties of complex numbers to simplify completely (7−√-64)+(6+3i)

Answer 1

To simplify the expression \( (7 - \sqrt{-64}) + (6 + 3i) \), we first need to simplify \( \sqrt{-64} \).

1. Simplify \( \sqrt{-64} \): \[ \sqrt{-64} = \sqrt{64} \cdot \sqrt{-1} = 8i \]

2. Replace \( \sqrt{-64} \) in the original expression: \[ (7 - \sqrt{-64}) + (6 + 3i) = (7 - 8i) + (6 + 3i) \]

3. Combine like terms:

   • Combine the real parts: \( 7 + 6 = 13 \)
   • Combine the imaginary parts: \( -8i + 3i = -5i \)

4. Write the final result: \[ 13 - 5i \]

Thus, the simplified expression is: \[ \boxed{13 - 5i} \]