# Complex Multiplication/Examples/(2 - 3i) (4 + 2i)

## Example of Complex Multiplication

$\paren {2 - 3 i} \paren {4 + 2 i} = 14 - 8 i$

## Proof

 $\displaystyle \paren {2 - 3 i} \paren {4 + 2 i}$ $=$ $\displaystyle \paren {2 \times 4 - \paren {-3} \times 2} + \paren {2 \times 2 + \paren {-3} \times 4} i$ Definition of Complex Multiplication $\displaystyle$ $=$ $\displaystyle \paren {8 + 6} + \paren {4 - 12} i$ $\displaystyle$ $=$ $\displaystyle 14 - 8 i$

$\blacksquare$