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

Question

Find the multiplicative inverse of 2 - 3i.

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Answer

Let $z=2-3 \mathrm{i}$
Then, $\bar{z}=2+3 \mathrm{i}$
and $|z|^2=2^2+(-3)^2=4+9=13$
Therefore, the multiplicative inverse of $2-3 \mathrm{i}$ is given by $z^{-1}=\frac{\bar{z}}{|z|^2}=\frac{2+3 i}{13}=\frac{2}{13}+\frac{3}{13} i$

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