# Complex Subtraction/Examples/(8 - 6i) - (2i - 7)

## Example of Complex Subtraction

$\paren {8 - 6 i} - \paren {2 i - 7} = 15 - 8 i$

## Proof

 $\ds \paren {8 - 6 i} - \paren {2 i - 7}$ $=$ $\ds \paren {8 + \paren {-6 i} } + \paren {-\paren {-7 + 2 i} }$ Definition of Complex Subtraction $\ds$ $=$ $\ds \paren {8 + \paren {-\paren {-7} } } + \paren {\paren {-6} + {\paren {-2} } } i$ Definition of Complex Addition $\ds$ $=$ $\ds \paren {8 + 7} + \paren {-6 - 2} i$ $\ds$ $=$ $\ds 15 - 8 i$

$\blacksquare$