Complex Modulus/Examples/-4+2i

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Example of Complex Modulus

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


Proof

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

$\blacksquare$


Sources