Question

How do you simplify `\frac { 8+ 6i } { 3- 2i }`?

Answer 1

`(12+34i)/13`

Explanation:

In order to simplify this, you need to make sure `i` isn't in the denominator (or bottom) of the fraction. To do this, multiply both the numerator and denominator by the conjugate of `3-2i`, which is `3+2i`. When doing this, make sure to use the FOIL method:

1)

`((8+6i) * (3+2i))/((3-2i) * (3+2i))`

2)

`(24+16i+18i-12)/(9+6i-6i-4i^2)`

Since `i` equals `sqrt(-1)`, `i^2` equals `-1`.

3)

`(12+34i)/(9+4)`

4)

`(12+34i)/(13)`