Question

Find the multiplicative inverse of the complex number $√5+3i$$$

Answer 1

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.)