Use the properties of complex numbers to simplify completely (7−−64−−−−√)+(6+3i) .(1 point)

Answer 1

To simplify the expression \( (7 - \sqrt{64}) + (6 + 3i) \), follow these steps:

1. Simplify \(\sqrt{64}\): \[ \sqrt{64} = 8 \] Thus, the expression becomes: \[ 7 - 8 + (6 + 3i) \]

2. Combine the real parts: \[ 7 - 8 = -1 \] So now the expression is: \[ -1 + (6 + 3i) \]

3. Combine like terms: \[ -1 + 6 = 5 \] Therefore, the expression simplifies to: \[ 5 + 3i \]

Thus, the final simplified expression is: \[ \boxed{5 + 3i} \]