Complex Modulus/Examples/z1 + z2/Proof 2
Jump to navigation
Jump to search
Example of Complex Modulus
- $\cmod {z_1 + z_2} = \sqrt {10}$
Proof
\(\ds \cmod {z_1 + z_2}\) | \(=\) | \(\ds \cmod {\paren {4 - 3 i} + \paren {-1 + 2 i} }\) | Definition of $z_1$ and $z_2$ | |||||||||||
\(\ds \) | \(=\) | \(\ds \cmod {\paren {4 - 1} + \paren {- 3 + 2} i}\) | Definition of Complex Addition | |||||||||||
\(\ds \) | \(=\) | \(\ds \cmod {3 - i}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \sqrt {3^2 + 1^2}\) | Definition of Complex Modulus | |||||||||||
\(\ds \) | \(=\) | \(\ds \sqrt {10}\) |
$\blacksquare$
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: $63 \ \text {(a)}$