Do I use the Foil method to find the product of (9-3i)(9+4i)?

of course. Just remember that i^2 = -1

81 + 36i -27i -12i^2

93 + 9i

i^2 = -1

Yes, you can use the FOIL method to find the product of (9-3i)(9+4i). The FOIL method is an acronym that stands for First, Outer, Inner, Last. It is a technique used to multiply two binomials.

To apply the FOIL method, you follow these steps:

1. Multiply the First terms: Take the first term from each binomial and multiply them together. In this case, it would be 9 * 9, which equals 81.

2. Multiply the Outer terms: Take the first term from the first binomial and the second term from the second binomial, and multiply them together. In this case, it would be 9 * 4i, which equals 36i.

3. Multiply the Inner terms: Take the second term from the first binomial and the first term from the second binomial, and multiply them together. In this case, it would be -3i * 9, which equals -27i.

4. Multiply the Last terms: Take the second term from each binomial and multiply them together. In this case, it would be -3i * 4i, which equals -12i^2. Remember that i^2 is equal to -1.

5. Combine the results: Add together the products from steps 1-4 to get the final result. In this case, it would be 81 + 36i - 27i - 12i^2.

Now, simplify the expression further. Since i^2 is equal to -1, you can substitute -1 for i^2:

81 + 36i - 27i - 12(-1) = 81 + 36i - 27i + 12 = 93 + 9i.

Therefore, the product of (9-3i)(9+4i) is 93 + 9i.