Question

simplify: 8/(3-i)

Answer 1

\[i = \sqrt{-1}\] so to solve this, you need to use the conjugate. Multiply 8/(3-i) by (3+i)/(3+i), and you can do this because it's essentially multiplying the expression by 1. Because of difference of squares, it will simplify. (3-i) * (3+i) = 3^2 +3i - 3i - i^2 = 3^2 - i^2 = 9 - (-1) = 10.

Therefore, your solution is [8*(3+i)]/10 = [4*(3+i)]/5 = (12+4i)/5.