Complex Modulus/Examples/z1 - z2/Proof 2

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Example of Complex Modulus

$\cmod {z_1 - z_2} = 5 \sqrt 2$


Proof

\(\ds \cmod {z_1 - z_2}\) \(=\) \(\ds \cmod {\paren {4 - 3 i} - \paren {-1 + 2 i} }\) Definition of $z_1$ and $z_2$
\(\ds \) \(=\) \(\ds \cmod {\paren {4 - \paren {-1} } + \paren {-3 - 2} i}\) Definition of Complex Subtraction
\(\ds \) \(=\) \(\ds \cmod {5 - 5 i}\)
\(\ds \) \(=\) \(\ds \sqrt {5^2 + 5^2}\) Definition of Complex Modulus
\(\ds \) \(=\) \(\ds 5 \sqrt 2\)

$\blacksquare$


Sources