Perform the indicated operation \& simplify. Express the answer as a complex number. \( (10-9 i)(3+4 i)=\square \)

To perform the operation \((10-9 i)(3+4 i)\), we can use the distributive property (also known as the FOIL method for binomials). 1. Multiply the real parts: \(10 \times 3 = 30\). 2. Multiply the outer parts: \(10 \times 4i = 40i\). 3. Multiply the inner parts: \(-9i \times 3 = -27i\). 4. Multiply the imaginary parts: \(-9i \times 4i = -36i^2\). (Remember that \(i^2 = -1\), so this becomes \(36\).) Now, add these results together: \[ 30 + 40i - 27i + 36 = 30 + 36 + (40i - 27i) = 66 + 13i. \] Hence, the simplified result is \(\boxed{66 + 13i}\).