Complex Multiplication/Examples/(2 - 3i) (4 + 2i)

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Example of Complex Multiplication

$\paren {2 - 3 i} \paren {4 + 2 i} = 14 - 8 i$


Proof

\(\displaystyle \paren {2 - 3 i} \paren {4 + 2 i}\) \(=\) \(\displaystyle \paren {2 \times 4 - \paren {-3} \times 2} + \paren {2 \times 2 + \paren {-3} \times 4} i\) Definition of Complex Multiplication
\(\displaystyle \) \(=\) \(\displaystyle \paren {8 + 6} + \paren {4 - 12} i\)
\(\displaystyle \) \(=\) \(\displaystyle 14 - 8 i\)

$\blacksquare$


Sources