Complex Modulus/Examples/-4+2i

Example of Complex Modulus

$\cmod {-4 + 2 i} = 2 \sqrt 5$


Proof

\(\ds \cmod {-4 + 2 i}\) \(=\) \(\ds \sqrt {\paren {-4}^2 + 2^2}\) Definition of Complex Modulus
\(\ds \) \(=\) \(\ds \sqrt {20}\)
\(\ds \) \(=\) \(\ds 2 \sqrt 5\)

$\blacksquare$


Sources

  • 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Absolute Value
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