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

From ProofWiki
Jump to navigation Jump to search

Example of Complex Addition

$\paren {5 + 3 i} + \paren {\paren {-1 + 2 i} + \paren {7 - 5 i} } = 11$


Proof

\(\displaystyle \paren {5 + 3 i} + \paren {\paren {-1 + 2 i} + \paren {7 - 5 i} }\) \(=\) \(\displaystyle \paren {5 + 3 i} + \paren {\paren {-1 + 7} + \paren {2 - 5} i}\) 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
\(\displaystyle \) \(=\) \(\displaystyle 11\)

$\blacksquare$


Sources