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  4. Find the multiplicative inverse of 2 - 3i.

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Q. Find the multiplicative inverse of $2 - 3i$.

Complex Numbers and Quadratic Equations

Solution:

Let $z = 2-3i$ , then, $z^{-1}=\frac{1}{2-3i}$
$=\frac{2+3i}{\left(2-3i\right)\left(2+3i\right)}$
$=\frac{2+3i}{2^{2}-\left(3i\right)^{2}}$
$=\frac{2+3i}{13}$
$=\frac{2}{13}+\frac{3}{13} i$