Complex Addition/Examples/(-3 + 5i) + (4 + 2i) + (5 - 3i) + (-4 - 6i)/Proof 1

Example of Complex Addition

$\paren {-3 + 5 i} + \paren {4 + 2 i} + \paren {5 - 3 i} + \paren {-4 - 6 i} = 2 - 2 i$

Proof

\(\ds \)

\(\)

\(\ds \paren {-3 + 5 i} + \paren {4 + 2 i} + \paren {5 - 3 i} + \paren {-4 - 6 i}\)

\(\ds \)

\(=\)

\(\ds \paren {\paren {-3} + 4 + 5 + \paren {-4} } + \paren {5 + 2 + \paren {-3} + \paren {-6} } i\)

Definition of Complex Addition

\(\ds \)

\(=\)

\(\ds 2 - 2 i\)

$\blacksquare$

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Solved Problems: Graphical Representation of Complex Numbers. Vectors: $5 \ \text{(c)}$