Complex Multiplication is Associative/Examples/(2 - i) ((-3 + 2i) (5 - 4i))

Examples of Use of Complex Multiplication is Associative

Example: $\paren {2 - i} \paren {\paren {-3 + 2 i} \paren {5 - 4 i} }$

$\paren {2 - i} \paren {\paren {-3 + 2 i} \paren {5 - 4 i} } = 8 + 51 i$

Example: $\paren {\paren {2 - i} \paren {-3 + 2 i} } \paren {5 - 4 i}$

$\paren {\paren {2 - i} \paren {-3 + 2 i} } \paren {5 - 4 i} = 8 + 51 i$

As can be seen:

$\paren {2 - i} \paren {\paren {-3 + 2 i} \paren {5 - 4 i} } = \paren {\paren {2 - i} \paren {-3 + 2 i} } \paren {5 - 4 i}$

$\blacksquare$

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: $1$