Complex Multiplication/Examples/(4 + 2i) (2 - 3i)
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Example of Complex Multiplication
- $\paren {4 + 2 i} \paren {2 - 3 i} = 14 - 8 i$
Proof
\(\ds \paren {4 + 2 i} \paren {2 - 3 i}\) | \(=\) | \(\ds \paren {4 \times 2 - 2 \times \paren {-3} } + \paren {2 \times 2 + 4 \times \paren {-3} } i\) | Definition of Complex Multiplication | |||||||||||
\(\ds \) | \(=\) | \(\ds \paren {8 + 6} + \paren {4 - 12} i\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 14 - 8 i\) |
$\blacksquare$
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: $1 \ \text {(g)}$