Complex Modulus of Reciprocal of Complex Number/Examples/5+12i

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Example of Complex Modulus of Reciprocal of Complex Number

$\left\vert{\dfrac 1 {5 + 12 i} }\right\rvert = \dfrac 1 {13}$


Proof

\(\ds \left\vert{\dfrac 1 {5 + 12 i} }\right\rvert\) \(=\) \(\ds \dfrac 1 {\left\vert{5 + 12 i}\right\rvert}\) Complex Modulus of Reciprocal of Complex Number
\(\ds \) \(=\) \(\ds \dfrac 1 {\sqrt{5^2 + 12^2} }\) Definition of Complex Modulus
\(\ds \) \(=\) \(\ds \dfrac 1 {\sqrt{169} }\)
\(\ds \) \(=\) \(\ds \dfrac 1 {13}\)

$\blacksquare$


Sources