Complex Arithmetic/Examples/3(1+2i) - 2(2-3i)/Proof 1
Jump to navigation
Jump to search
Example of Complex Arithmetic
- $3 \paren {-1 + 4 i} - 2 \paren {7 - i} = -17 + 14 i$
Proof
| \(\ds 3 \paren {1 + 2 i} - 2 \paren {2 - 3 i}\) | \(=\) | \(\ds \paren {3 \times 1 + 3 \times 2 i} - \paren {2 \times 2 - 2 \times 3 i}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {3 + 6 i} - \paren {4 - 6 i}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {3 - 4} + \paren {6 - \paren {-6} } i\) | Definition of Complex Subtraction | |||||||||||
| \(\ds \) | \(=\) | \(\ds -1 + 12 i\) |
$\blacksquare$
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Graphical Representation of Complex Numbers. Vectors: $61 \ \text {(c)}$