Simplify $\displaystyle\frac{1-i}{2+3i}$, where $i=\sqrt{-1}$ is the imaginary unit.
\(\frac{1-i}{2+3i}\) Multiply top/bottom by 2 - 3i
[ 1 - i ] [ 2 - 3i ] / [ ( 2 + 3i) ( 2 - 3i) ]
[ 2 - 2i - 3i + 3i^2 ] / [ 4 - 9i^2 ]
[ 2 - 3 - 2i - 3i ] / [ 4 + 9 ]
[ -1 - 5i ] / [ 13 ]
