# Complex Division/Examples/(2 - 3i) (4 - i)^-1

## Example of Complex Division

$\dfrac {2 - 3 i} {4 - i} = \dfrac {11} {17} - \dfrac {10} {17} i$

## Proof

 $\ds \dfrac {2 - 3 i} {4 - i}$ $=$ $\ds \dfrac {\paren {2 - 3 i} \paren {4 + i} } {\paren {4 - i} \paren {4 + i} }$ multiplying top and bottom by $4 + i$ $\ds$ $=$ $\ds \dfrac {8 - 12 i + 2 i - 3 i^2} {4^2 + 1^2}$ simplifying $\ds$ $=$ $\ds \dfrac {11 - 10 i} {17}$ simplifying

$\blacksquare$