# Inverse for Complex Multiplication/Examples/3+2i

## Example of Inverse for Complex Multiplication

$\dfrac 1 {3 + 2 i} = \dfrac 3 {13} + \dfrac {2 i} {13}$

## Proof

 $\ds \dfrac 1 {3 + 2 i}$ $=$ $\ds \dfrac {3 - 2 i} {\paren {3 + 2 i} \paren {3 - 2 i} }$ multiplying top and bottom by $3 - 2 i$ $\ds$ $=$ $\ds \dfrac {3 - 2 i} {3^2 + 2^2}$ simplifying $\ds$ $=$ $\ds \dfrac {3 - 2 i} {13}$ simplifying

$\blacksquare$