**Question: **Find the conjugate of $\frac{1}{(3+4 \mathrm{i})}$.

**Solution:**
Let $\mathrm{z}=\frac{1}{3+4 \mathrm{i}}$

$=\frac{1}{3+4 i} \times \frac{3-4 i}{3-4 i}=\frac{3-4 i}{9+16}$

$=\frac{3}{25}-\frac{4}{25} i$

$\Rightarrow \bar{z}=\frac{3}{25}+\frac{4}{25} i$