Multiply. \( (-4+9 i)(8-5 i) \) \( (-4+9 i)(8-5 i)=\square \) (Simplify your answer. Type your answer in the form a + bi.)

To multiply the complex numbers \((-4 + 9i)\) and \((8 - 5i)\), we use the distributive property (also known as the FOIL method for binomials): \[ (-4)(8) + (-4)(-5i) + (9i)(8) + (9i)(-5i) \] Calculating each term: 1. \((-4)(8) = -32\) 2. \((-4)(-5i) = 20i\) 3. \((9i)(8) = 72i\) 4. \((9i)(-5i) = -45i^2\) (Since \(i^2 = -1\), this becomes \(+45\)) Now, combine all these results: \[ -32 + 20i + 72i + 45 \] Combining like terms: 1. Real parts: \(-32 + 45 = 13\) 2. Imaginary parts: \(20i + 72i = 92i\) Thus, the final result is: \[ (-4 + 9i)(8 - 5i) = 13 + 92i \] So, the answer is \( \boxed{13 + 92i} \).