Find the multiplicative inverse of $2 - 3 i$

2 + 3 i

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\frac{2 + 3 i}{13}

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- 2 - 3 i

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3 i

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Solution

The correct option is B $\frac{2 + 3 i}{13}$
Let $Z_{i}$ be the multiplicative Inverse of $2 - 3 i$

so that,
$Z_{i} (2 - 3 i) = 1 \Rightarrow Z_{i} = \frac{1}{2 - 3 i} = \frac{2 + 3 i}{(2 - 3 i) (2 + 3 i)} = \frac{2 + 3 i}{2^{2} - (- 3^{2})} = \frac{2 + 3 i}{(2 - 3 i) (2 + 3 i)} = \frac{2 + 3 i}{2^{2} + 3^{2}} = \frac{2}{13} + \frac{3 i}{13}$

Suggest Corrections

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