Remember FOIL? If not, it stands for first, outer, inner, last. This basically means you multiply the first number in each set, then the inner numbers, then the outer numbers, then the last numbers, stick 'em together, and you have your answer. I'll illustrate!
(5 - 7i)(2 + 4i)
The first numbers are 5 and 2, so we multiply those to get 10.
The inner numbers are -7i and 2, so we multiply those to get -14i.
The outer numbers are 5 and 4i, so we multiply those to get 20i.
Finally, the last numbers are -7i and 4i, so we multiply those to get -28i².
Our equation now is 10 - 14i + 20i - 28i².
Now to simplify! By combining terms we get:
10 + 6i - 28i²
And because (√-1)², or i², is equal to -1, -28i² becomes a positive 28. Now we can add that in to get:
38i + 6, or letter D, as our final answer.
Hope this helped!
