Complex Modulus/Examples/1+i
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Example of Complex Modulus
- $\cmod {1 + i} = \sqrt 2$
Proof
| \(\ds \cmod {1 + i}\) | \(=\) | \(\ds \cmod {1 + 1 i}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \sqrt {1^2 + 1^2}\) | Definition of Complex Modulus | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sqrt 2\) |
$\blacksquare$
Sources
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.2$. The Algebraic Theory: Examples