Question

How do you evaluate `(6+ 8i ) ( 1- 3i )`?

Answer 1

30-10i

Explanation:

You would evaluate this just as you would evaluate the multiplication of binomials. Many people like to use the FOIL method (multiplying together the first, then outer, then inner, then last terms together and adding up all of the products) but I like to think about it as multiplying everything in the first group by everything in the second group. (These two methods do the same thing, but that's just how I like to think about it.)

After expanding this, we get `6-18i+8i-24i^2`. Remember, `i` is defined as the square root of -1, so `i^2=-1`. Using this, we can rewrite the equation as `6-18i+8i+24`, and combine like terms to get `30-10i` as our final answer.