Perform the indicated operation \& simplify. Express the answer in terms of \( i \) (as a complex number). \( (1-5 i)(-10-11 i)= \)

To perform the indicated operation, we need to multiply the two complex numbers: \[ (1 - 5i)(-10 - 11i) \] Using the distributive property (also known as the FOIL method for binomials), we get: \[ 1 \cdot (-10) + 1 \cdot (-11i) - 5i \cdot (-10) - 5i \cdot (-11i) \] Calculating each term separately: 1. \( 1 \cdot (-10) = -10 \) 2. \( 1 \cdot (-11i) = -11i \) 3. \( -5i \cdot (-10) = 50i \) 4. \( -5i \cdot (-11i) = 55i^2 \) (remember that \( i^2 = -1 \), so this term becomes \( -55 \)) Now, combine these results: \[ -10 - 11i + 50i - 55 \] Combine like terms: - Combine the real parts: \(-10 - 55 = -65\) - Combine the imaginary parts: \(-11i + 50i = 39i\) The simplified expression is: \[ -65 + 39i \]