Find the multiplicative inverse of the complex number –i
Question:
Find the multiplicative inverse of the complex number $-i$
Solution:
Let $z=-i$
Then, $\bar{z}=i$ and $|z|^{2}=1^{2}=1$
Therefore, the multiplicative inverse of $-i$ is given by
$z^{-1}=\frac{\bar{z}}{|z|^{2}}=\frac{i}{1}=i$