Question

Find the conjugate of the following complex number:

\[\frac{1}{3 + 5i}\]

Answer 1

\[\text {  Let }z = \frac{1}{3 + 5i}\]

\[ = \frac{1}{3 + 5i} \times \frac{3 - 5i}{3 - 5i}\]

\[ = \frac{3 - 5i}{9 - 25 i^2}\]

\[ = \frac{3 - 5i}{9 + 25}\]

\[ = \frac{3 - 5i}{34}\]

\[ \therefore \bar{z} = \frac{3 + 5i}{34}\]