The product of two expressions and the complex number i is equal to 12. (expression A)(expression B) × i  =  12

Sure, but you haven't provided any specific expressions for A and B. The product of two expressions and the complex number i could be a variety of things depending on what those expressions are.

However, if we assume that the expressions A and B are real numbers, then we can say that the product of A and B must be -12. This is because when you multiply a real number by the imaginary unit i, the result is an imaginary number. So, if (A)(B)i = 12, then (A)(B) must be -12 because i is the square root of -1.

Here are the steps:

1. Set up the equation: (A)(B)i = 12
2. Divide both sides by i: (A)(B) = 12/i
3. Simplify the right side: (A)(B) = -12 (since i is the square root of -1)
4. Therefore, the product of the expressions A and B must be -12.

Please provide the specific expressions for A and B if you need a more specific answer.