# Complex Addition/Examples/(5 + 3i) + ((-1 + 2i) + (7 - 5i))

$\paren {5 + 3 i} + \paren {\paren {-1 + 2 i} + \paren {7 - 5 i} } = 11$
 $\displaystyle \paren {5 + 3 i} + \paren {\paren {-1 + 2 i} + \paren {7 - 5 i} }$ $=$ $\displaystyle \paren {5 + 3 i} + \paren {\paren {-1 + 7} + \paren {2 - 5} i}$ Definition of Complex Addition $\displaystyle$ $=$ $\displaystyle \paren {5 + 3 i} + \paren {6 - 3 i}$ simplification $\displaystyle$ $=$ $\displaystyle \paren {5 + 6} + \paren {3 i - 3 i}$ Definition of Complex Addition $\displaystyle$ $=$ $\displaystyle 11$
$\blacksquare$