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

Example of Complex Arithmetic

$3 \paren {1 + i} + 2 \paren {4 - 3 i} - \paren {2 + 5 i} = 9 - 8 i$

Proof

\(\ds \)

\(\)

\(\ds 3 \paren {1 + i} + 2 \paren {4 - 3 i} - \paren {2 + 5 i}\)

\(\ds \)

\(=\)

\(\ds \paren {3 + 3} + \paren {8 - 6 i} - \paren {2 + 5 i}\)

\(\ds \)

\(=\)

\(\ds \paren {\paren 3 + 8 - 2} + \paren {3 - 6 - 5} i\)

\(\ds \)

\(=\)

\(\ds 9 - 8 i\)

$\blacksquare$

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Graphical Representation of Complex Numbers. Vectors: $61 \ \text {(d)}$