Complex Multiplication/Examples/(3+2i)(2-i)

Example of Complex Multiplication

$\paren {3 + 2 i} \paren {2 - i} = 8 + i$

Proof

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

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 8 + i\)

$\blacksquare$

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Fundamental Operations with Complex Numbers: $53 \ \text {(c)}$