Complex Multiplication Distributes over Addition/Examples/(2 - i) ((-3 + 2i) (5 - 4i))

Examples of Use of Complex Multiplication Distributes over Addition

Example: $\paren {-1 + 2 i} \paren {\paren {7 - 5 i} + \paren {-3 + 4 i} }$

$\paren {-1 + 2 i} \paren {\paren {7 - 5 i} + \paren {-3 + 4 i} } = -2 + 9 i$

Example: $\paren {-1 + 2 i} \paren {7 - 5 i} + \paren {-1 + 2 i} \paren {-3 + 4 i}$

$\paren {-1 + 2 i} \paren {7 - 5 i} + \paren {-1 + 2 i} \paren {-3 + 4 i} = -2 + 9 i$

As can be seen:

$\paren {-1 + 2 i} \paren {\paren {7 - 5 i} + \paren {-3 + 4 i} } = \paren {-1 + 2 i} \paren {7 - 5 i} + \paren {-1 + 2 i} \paren {-3 + 4 i}$

$\blacksquare$

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