Question:
Find the conjugate of $\frac{1}{(3+4 \mathrm{i})}$.
Solution:
Let $\mathrm{z}=\frac{1}{3+4 \mathrm{i}}$
$=\frac{1}{3+4 i} \times \frac{3-4 i}{3-4 i}=\frac{3-4 i}{9+16}$
$=\frac{3}{25}-\frac{4}{25} i$
$\Rightarrow \bar{z}=\frac{3}{25}+\frac{4}{25} i$
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