Complex Modulus/Examples/i

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Example of Complex Modulus

$\cmod i = \cmod {-i} = 1$


Proof

\(\displaystyle \cmod i\) \(=\) \(\displaystyle \cmod {0 + 1 i}\)
\(\displaystyle \) \(=\) \(\displaystyle \sqrt {0^2 + 1^2}\) Definition of Complex Modulus
\(\displaystyle \) \(=\) \(\displaystyle \sqrt 1\)
\(\displaystyle \) \(=\) \(\displaystyle 1\)


\(\displaystyle \cmod {-i}\) \(=\) \(\displaystyle \cmod {0 + \left({-1}\right) i}\)
\(\displaystyle \) \(=\) \(\displaystyle \sqrt {0^2 + \left({-1}\right)^2}\) Definition of Complex Modulus
\(\displaystyle \) \(=\) \(\displaystyle \sqrt 1\)
\(\displaystyle \) \(=\) \(\displaystyle 1\)

$\blacksquare$


Sources