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
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1$. Algebraic Theory of Complex Numbers: Exercise $4 \ \text{(iii)}$