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

\(\displaystyle \paren {1 + 2 i} \paren {3 + 4 i}\) \(=\) \(\displaystyle \paren {1 \times 3 - 2 \times 4} + \paren {1 \times 4 + 2 \times 3} i\)
\(\displaystyle \) \(=\) \(\displaystyle \paren {3 - 8} + \paren {4 + 6} i\)
\(\displaystyle \) \(=\) \(\displaystyle -5 + 10 i\)

$\blacksquare$


Sources