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

Example of Complex Addition

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

Proof

\(\ds \paren {5 + 3 i} + \paren {\paren {-1 + 2 i} + \paren {7 - 5 i} }\)

\(=\)

\(\ds \paren {5 + 3 i} + \paren {\paren {-1 + 7} + \paren {2 - 5} i}\)

Definition of Complex Addition

\(\ds \)

\(=\)

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

simplification

\(\ds \)

\(=\)

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

Definition of Complex Addition

\(\ds \)

\(=\)

\(\ds 11\)

$\blacksquare$

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Solved Problems: Fundamental Operations with Complex Numbers: $1 \ \text {(d)}$