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