Complex Multiplication/Examples/(1+2i)(3+4i)
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Example of Complex Multiplication
- $\paren {1 + 2 i} \paren {3 + 4 i} = -5 + 10 i$
Proof
| \(\ds \paren {1 + 2 i} \paren {3 + 4 i}\) | \(=\) | \(\ds \paren {1 \times 3 - 2 \times 4} + \paren {1 \times 4 + 2 \times 3} i\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {3 - 8} + \paren {4 + 6} i\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -5 + 10 i\) |
$\blacksquare$
Sources
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1$. Algebraic Theory of Complex Numbers: Exercise $1 \ \text{(i)}$