Let \(z=√5+3i\)
Then,
\(z¯=√5-3i\)
\(|z|^{2}=(√5)^2+(3)^2 =14\)
Therefore the multiplicative inverse of \(4-3i\)
\(z^{-1}=\dfrac{z¯}{|z|^{2}}\)
\(=\dfrac{√5-3i}{14}\)
\(=\dfrac{√5}{14}-\dfrac{3}{14}i\) (Ans.)