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.)