Complex Multiplication/Examples/(4+i)(3+2i)(1-i)
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Example of Complex Multiplication
- $\paren {4 + i} \paren {3 + 2 i} \paren {1 - i} = 21 + i$
Proof
\(\ds \paren {4 + i} \paren {3 + 2 i} \paren {1 - i}\) | \(=\) | \(\ds \paren {4 + i} \paren {\paren {3 \times 1 - 2 \times \paren {-1} } + \paren {3 \times \paren {-1} + 2 \times 1} i}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {4 + i} \paren {5 - i}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {4 \times 5 - 1 \times + \paren {-1} } + \paren {4 \times \paren {-1} + 1 \times 5}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 21 + i\) |
$\blacksquare$
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: $53 \ \text {(f)}$