Complex Multiplication/Examples/(4+i)(3+2i)(1-i)

Example of Complex Multiplication

$\paren {4 + i} \paren {3 + 2 i} \paren {1 - i} = 21 + i$

$\ds \paren {4 + i} \paren {3 + 2 i} \paren {1 - i}$

$=$

$\ds \paren {4 + i} \paren {\paren {3 \times 1 - 2 \times \paren {-1} } + \paren {3 \times \paren {-1} + 2 \times 1} i}$

$\ds $

$=$

$\ds \paren {4 + i} \paren {5 - i}$

$\ds $

$=$

$\ds \paren {4 \times 5 - 1 \times + \paren {-1} } + \paren {4 \times \paren {-1} + 1 \times 5}$

$\ds $

$=$

$\ds 21 + i$

$\blacksquare$

1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Fundamental Operations with Complex Numbers: $53 \ \text {(f)}$