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.)