Hi Jasmine,
To simply this, we should FOIL as if it were any other pair of parentheses. The first numbers, 4 and 2, multiply to give 8. The outer numbers, 4 and i, multiply to become 4i. The inner numbers, -5i and 2, multiply and result in -10i. And the last numbers, -5i and i, multiply to give -5i^2. Our entire expression is 8 + 4i - 10i -5i^2. However, we can combine like terms; 4i - 10i gives -6i. Also, when we square the imaginary number i, we obtain -1, so -5i^2 = -5(-1) = +5. That 5 adds to 8 and equals 13. Our simplified expression is 13 - 6i.
Hope this helped!
Kevin
