Question

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:
\[
\boxed{5 + 3i}
\]