Find multiplicative inverse of $3 + 2 i$

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Solution

Let $z$ be the multiplicative inverse of $3 + 2 i .$ then
$\Rightarrow$ $z . (3 + 2 i) = 1 \Rightarrow z = \frac{1}{3 + 2 i} = \frac{3 - 2 i}{(3 + 2 i) (3 - 2 i)}$
$\Rightarrow$ $z = \frac{3}{13} - \frac{2}{13} i$
$(\frac{3}{13} - \frac{2}{13} i)$

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