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Question
Find the multiplicative inverse of the complex number:
4 – 3i
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Solution
Multiplicative inverse of `4 - 3i = 1/(4-3i)`
\[ z = 4 - 3i\]
\[\text { Then,} \frac{1}{z} = \frac{1}{4 - 3i} \times \frac{4 + 3i}{4 + 3i}\]
\[ = \frac{4 + 3i}{16 - 9 i^2}\]
\[ = \frac{4 + 3i}{25}\]
\[ = \frac{4}{25} + \frac{3}{25}i\]
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