Complex Arithmetic/Examples/3(-1+4i) - 2(7-i)
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Example of Complex Arithmetic
- $3 \paren {-1 + 4 i} - 2 \paren {7 - i} = -17 + 14 i$
Proof
| \(\ds 3 \paren {-1 + 4 i} - 2 \paren {7 - i}\) | \(=\) | \(\ds \paren {3 \times -1 + 3 \times 4 i} - \paren {2 \times 7 - 2 \times i}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {-3 + 12 i} - \paren {14 - 2 i}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {-3 - 14} + \paren {12 - \paren {-2} } i\) | Definition of Complex Subtraction | |||||||||||
| \(\ds \) | \(=\) | \(\ds -17 + 14 i\) |
$\blacksquare$
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Fundamental Operations with Complex Numbers: $53 \ \text {(b)}$