Question

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

Answer 1

Let the mutiplicative inverse of $-i$ be $x$

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

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

$\Rightarrow x=\frac{i}{-i^2}$

$\Rightarrow x=\frac{i}{-(-1)}$

$\Rightarrow x=i$

Thus, the the mutiplicative inverse of $-i$ is $i$