Find the multiplicative inverse of the complex numbers given.
$\sqrt{5} + 3 i$ .

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Solution

$\begin{matrix} (\sqrt{5 + 3 i}) M u l t i p l i c a t i v e i n v e r s e i n \Rightarrow \frac{i}{(\sqrt{5} + 3 i)} \times \frac{\sqrt{5} - 3 i}{(\sqrt{5} - 3 i)} \Rightarrow \frac{\sqrt{5} - 3 i}{5 - 9 i^{2}} = \frac{\sqrt{5} - 3 i}{5 + 9} = \frac{\sqrt{5} - 3 i}{14} = \frac{\sqrt{5}}{14} \frac{- 3 i}{14} A n s . \end{matrix}$

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