Complex Conjugate/Examples/conj z1 - conj z2/Proof 2
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Example of Complex Conjugates
- $\overline {z_1} - \overline {z_2} = 5 + 5 i$
Proof
| \(\ds \overline {z_1} - \overline {z_2}\) | \(=\) | \(\ds \paren {\overline {4 - 3 i} } - \paren {\overline {-1 + 2 i} }\) | Definition of $z_1$ and $z_2$ | |||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {4 + 3 i} - \paren {-1 - 2 i}\) | Definition of Complex Conjugate | |||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {4 - \paren {-1} } + \paren {3 - \paren {-2} } i\) | Definition of Complex Subtraction | |||||||||||
| \(\ds \) | \(=\) | \(\ds 5 + 5 i\) |
$\blacksquare$
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: $63 \ \text {(c)}$