Question

Find the multiplicative inverse of the complex number $-i$

Answer 1

Let $z=-i$

Then,

$z¯=-i$

$|z|^{2}=1$

Therefore the multiplicative inverse of $-i$

$z^{-1}=\dfrac{z¯}{|z|^{2}}$

$=\dfrac{i}{1}$

$=i$ (Ans.)