Complex Arithmetic/Examples/1 2^-1 (4-3i) + 3 2^-1 (5+2i)/Proof 1
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Example of Complex Arithmetic
- $\dfrac 1 2 \paren {4 - 3 i} + \dfrac 3 2 \paren {5 + 2 i} = \dfrac {19} 2 + \dfrac 3 2 i$
Proof
| \(\ds \) | \(\) | \(\ds \dfrac 1 2 \paren {4 - 3 i} + \dfrac 3 2 \paren {5 + 2 i}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {2 - \dfrac 3 2 i} + \paren {\dfrac {15} 2 + 3 i}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {\paren 2 + \dfrac {15} 2} + \paren {-\dfrac 3 2 + 3} i\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {19} 2 + \dfrac 3 2 i\) |
$\blacksquare$
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: $61 \ \text {(e)}$