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 $\displaystyle$ $=$ $\displaystyle \sqrt {20}$ $\displaystyle$ $=$ $\displaystyle 2 \sqrt 5$

$\blacksquare$