Question

Find the multiplicative inverse of each of the complex numbers given in the Exercises $11$ to $13$.
$-i$

Answer 1

$\Rightarrow$ Multiplicative inverse of $z=z^{-1}$

$\Rightarrow$ Multiplicative inverse of $z=\frac{1}{z}$

Putting $z=-i$

$\Rightarrow$ Multiplicative inverse of $-i=\frac{1}{-i}$

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

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

$=\frac{i}{-(-1)}$ [ Putting $i^2=-1$ ]

$=i$