Use foil to solve this problem.
Basically you want to multiply the second parentheses (5+6i) by the first parentheses (-6-3i). You can show this using the distributive method. Here's how it looks like:
-6(5+6i) - 3i(5+6i)
1. Distribute -6 inside the parentheses first.
(-30-36i) - 3i(5+6i)
*Here's something I think you should know: i times i (or i squared) is equal to negative 1.*
2. Now distribute -3i inside the parentheses.
To multiply -3i and 6i, you'll cancel the i values and make the i attached to the 6i become a -1, so now you have -3 times 6(-1), which is -3 * -6 = 18. This is why I have +18 in the second parentheses.
-30-36i - 15i+18
3. Remove the parentheses.
-30 - 36i - 15i + 18
4. Combine like terms.
-30+18 = -12
-36i-15i = -51i
-12-51i
Answer is:
-12 - 51i
