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

Example of Complex Multiplication

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

Proof

\(\ds \paren {2 - 3 i} \paren {4 + 2 i}\)

\(=\)

\(\ds \paren {2 \times 4 - \paren {-3} \times 2} + \paren {2 \times 2 + \paren {-3} \times 4} i\)

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: $1 \ \text {(f)}$