Inverse for Complex Multiplication/Examples/3+2i

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Example of Inverse for Complex Multiplication

$\dfrac 1 {3 + 2 i} = \dfrac 3 {13} + \dfrac {2 i} {13}$


Proof

\(\ds \dfrac 1 {3 + 2 i}\) \(=\) \(\ds \dfrac {3 - 2 i} {\paren {3 + 2 i} \paren {3 - 2 i} }\) multiplying top and bottom by $3 - 2 i$
\(\ds \) \(=\) \(\ds \dfrac {3 - 2 i} {3^2 + 2^2}\) simplifying
\(\ds \) \(=\) \(\ds \dfrac {3 - 2 i} {13}\) simplifying

$\blacksquare$


Sources