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

Question

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

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Answer

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

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