Question

Find the multiplicative inverse of the complex number \( 4 - 3i\)

Answer 1

Let \(z=4-3i\)

Then,

\(z¯=4+3i\)

\(|z|^{2}=4^2+(-3)^2 =25\)

Therefore the multiplicative inverse of \(4-3i\)

\(z^{-1}=\dfrac{z¯}{|z|^{2}}\)

\(=\dfrac{4+3i}{25}\)

\(=\dfrac{4}{25}+\dfrac{3}{25}i\)   (Ans.)