Complex Modulus/Examples/z1 - z2/Proof 2
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Example of Complex Modulus
- $\cmod {z_1 - z_2} = 5 \sqrt 2$
Proof
\(\ds \cmod {z_1 - z_2}\) | \(=\) | \(\ds \cmod {\paren {4 - 3 i} - \paren {-1 + 2 i} }\) | Definition of $z_1$ and $z_2$ | |||||||||||
\(\ds \) | \(=\) | \(\ds \cmod {\paren {4 - \paren {-1} } + \paren {-3 - 2} i}\) | Definition of Complex Subtraction | |||||||||||
\(\ds \) | \(=\) | \(\ds \cmod {5 - 5 i}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \sqrt {5^2 + 5^2}\) | Definition of Complex Modulus | |||||||||||
\(\ds \) | \(=\) | \(\ds 5 \sqrt 2\) |
$\blacksquare$
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: $63 \ \text {(b)}$