Complex Division/Examples/(3+4i) (1+2i)^-1

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Example of Complex Division

$\dfrac {3 + 4 i} {1 + 2 i} = \dfrac {11} 5 - \dfrac 2 5 i$


Proof

\(\ds \dfrac {3 + 4 i} {1 + 2 i}\) \(=\) \(\ds \dfrac {\paren {3 + 4 i} \paren {1 - 2 i} } {\paren {1 + 2 i} \paren {1 - 2 i} }\) multiplying top and bottom by $1 - 2 i$
\(\ds \) \(=\) \(\ds \dfrac {3 + 4 i - 6 i - 8 i^2} {1^2 + 2^2}\) simplifying
\(\ds \) \(=\) \(\ds \dfrac {11 - 2 i} 5\) simplifying

$\blacksquare$


Sources