Question

How do you simplify `(4-4i)/(5+3i)`?

Answer 1

`2/9-8/9i`

Explanation:

Use the conjugate of the denominator. (Recall that the conjugate of `a+b` is `a-b`.)

We can multiply the expression by `(5-3i)/(5-3i)`.

`(4-4i)/(5+3i)((5-3i)/(5-3i))=(20-20i-12i+12i^2)/(25cancel(-15i+15i)-9i^2)=(20-32i+12i^2)/(25-9i^2)`

Recall that `i=sqrt1`, so `i^2=-1`.

`(20-32i+12(-1))/(25-9(-1))=(20-12-32i)/(25+9)=(8-32i)/36=2/9-8/9i`

Note that the answer is written in the complex number format `a+bi`.