\( (12 \sqrt{-8})(-5 \sqrt{-9})=\square \) (Type an exact answer, using radicals as needed. Type your answer in the form \( a+b i \).)

To solve the expression \( (12 \sqrt{-8})(-5 \sqrt{-9}) \), we first simplify the square roots of the negative numbers. 1. Simplifying \( \sqrt{-8} \): \[ \sqrt{-8} = \sqrt{8} \cdot i = \sqrt{4 \cdot 2} \cdot i = 2\sqrt{2} \cdot i \] 2. Simplifying \( \sqrt{-9} \): \[ \sqrt{-9} = \sqrt{9} \cdot i = 3 \cdot i \] Now substituting these back into the original expression: \[ (12 \cdot 2\sqrt{2} i)(-5 \cdot 3 i) \] Calculating the coefficients first: \[ = (12 \cdot 2 \cdot -5 \cdot 3) \cdot (i \cdot i) = (-360) \cdot (i^2) \] Since \( i^2 = -1 \), we can replace \( i^2 \) with \(-1\): \[ = -360 \cdot (-1) = 360 \] Thus, we now have a real number, and can express it in the desired form \( a + bi \): \[ = 360 + 0i \] So, the final answer is: \[ \boxed{360 + 0i} \]