Question

Find the multiplicative inverse of the complex numbers given the following:
$4-3i$

Answer 1

Let multiplicative inverse of $4-3i$ be $x$

$\Rightarrow x=\frac{1}{4-3i}$

Rationalize the denominator

$\Rightarrow x=\frac{1}{4-3i}\times \frac{4+3i}{4+3i}$

$\Rightarrow x=\frac{4+3i}{4^2-(3i{)}^2}$

$\Rightarrow x=\frac{4+3i}{16-(-9)}=\frac{4+3i}{16+9}$

$\Rightarrow x=\frac{4+3i}{25}$

The multiplicative inverse of $4-3i$ is $\frac{4+3i}{25}$