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Question
Find the conjugate of the following complex number:
\[\frac{1}{1 + i}\]
Solution
\[\text { Let } z = \frac{1}{1 + i}\]
\[ = \frac{1}{1 + i} \times \frac{1 - i}{1 - i}\]
\[ = \frac{1 - i}{1 - i^2}\]
\[ = \frac{1 - i}{2}\]
\[ \Rightarrow \bar{z} = \frac{1 + i}{2}\]
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