10.2 Find the number conjugate to the number $z=\frac{2 \sqrt{3}-i}{\sqrt{3}+i}+3$.
10.2 Multiplying the numerator and the denominator of the fraction by the expression $\sqrt{3}-i$, the conjugate of the denominator, we get

$$
\begin{aligned}
& z=\frac{(2 \sqrt{3}-i)(\sqrt{3}-i)}{(\sqrt{3}+i)(\sqrt{3}-i)}+3=\frac{6-2 \sqrt{3} i-\sqrt{3} i-1}{4}+3= \\
& =\frac{5-3 \sqrt{3} i}{4}+3=\frac{17}{4}-\frac{3 \sqrt{3}}{4} i
\end{aligned}
$$

from which $\bar{z}=\frac{17}{4}+\frac{3 \sqrt{3}}{4} i$.

Answer: $4.25+0.75 \sqrt{3} i$.