Question

How do you evaluate `\frac { 6+ i } { 2- 3i } =`?

Answer 1

`(9-20i)/13`

Explanation:

Multiply the fraction by `1` in the form of `(2+3i)/(2+3i)` (`2+3i` is the complex conjugate of the denominator) to get `i` out of the denominator.

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

Multiply out and combine like terms, keeping in mind that `i^2="-"1`

`(12+18i+2i-3)/(4+6i-6i+9)=(9-20i)/13`