Question

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

• A. $\sqrt{5}-3i$
• B. $\frac{\sqrt{5}-3i}{14}$
• C. $-\sqrt{5}+3i$
• D. $\frac{-\sqrt{5}+3i}{14}$

Answer 1

Answer: (B)

$\frac{\sqrt{5}-3i}{14}$

$\sqrt{5}+3i$

$(\sqrt{5}+3i{)}^{-1}$ is the inverse

$=\frac{1}{\sqrt{5}+3i}$

On rationalizing,

$=\frac{\sqrt{5}-3i}{5-9i^2}$

$=\frac{\sqrt{5}-3i}{5+9}$

$=\frac{\sqrt{5}-3i}{14}$