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Question
Find the multiplicative inverse of the following complex number:
1 − i
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Solution
\[\text{ Let} z = 1 - i . \text { Then} , \]
\[\frac{1}{z} = \frac{1}{1 - i}\]
\[ = \frac{1}{1 - i} \times \frac{1 + i}{1 + i}\]
\[ = \frac{1 + i}{1 - i^2}\]
\[ = \frac{1}{2}\left( 1 + i \right)\]
\[ = \frac{1}{2} + \frac{1}{2}i\]
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