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

Example of Complex Addition

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

Proof

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

\(=\)

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

Definition of Complex Addition

\(\ds \)

\(=\)

\(\ds \paren {4 + 5 i} + \paren {7 - 5 i}\)

simplification

\(\ds \)

\(=\)

\(\ds \paren {4 + 7} + \paren {5 i - 5 i}\)

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: $1 \ \text {(e)}$