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Question
Find the conjugate of the following complex number:
\[\frac{1}{3 + 5i}\]
Solution
\[\text { Let }z = \frac{1}{3 + 5i}\]
\[ = \frac{1}{3 + 5i} \times \frac{3 - 5i}{3 - 5i}\]
\[ = \frac{3 - 5i}{9 - 25 i^2}\]
\[ = \frac{3 - 5i}{9 + 25}\]
\[ = \frac{3 - 5i}{34}\]
\[ \therefore \bar{z} = \frac{3 + 5i}{34}\]
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