To simplify the expression \( (7 - \sqrt{64}) + (6 + 3i) \), we first need to handle the term \( \sqrt{64} \).
The square root of 64 is 8, so we have:
\[ (7 - 8) + (6 + 3i) \]
Now simplify \( 7 - 8 \):
\[ -1 + (6 + 3i) \]
Next, we combine the real parts and the imaginary parts:
Real part: \( -1 + 6 = 5 \)
Imaginary part: \( 3i \)
Thus, we can now write the expression as:
\[ 5 + 3i \]
This doesn't appear to match any of the provided options. However, if we recheck the choices:
- 13 + 11i
- 8i
- 13 - 5i
- 1 - 5i
None of these options equal \( 5 + 3i \). The calculation seems correct. Please confirm the original expression for any typographical errors. If \( (7 - \sqrt{64}) + (6 + 3i) \) is accurate, the simplified expression is \( 5 + 3i \), which does not match the given options.