3. Given the complex number sequence $\left\{z_{n}\right\}$ satisfies
$$
z_{1}=1, z_{n+1}=\overline{z_{n}}+1+n \mathrm{i}(n=1,2, \cdots),
$$

where $\mathrm{i}$ is the imaginary unit, and $\overline{z_{n}}$ denotes the complex conjugate of $z_{n}$. Then the value of $z_{2015}$ is $\qquad$ .
3. $2015+1007 \mathrm{i}$.

From the given, for all positive integers $n$, we have
$$
\begin{array}{l}
z_{n+2}=\overline{z_{n+1}}+1+(n+1) \mathrm{i} \\
==\overline{\overline{z_{n}}+1+n \mathrm{i}}+1+(n+1) \mathrm{i}=z_{n}+2+\mathrm{i} \\
\text { Therefore, } z_{2015}=z_{1}+1007(2+\mathrm{i})=2015+1007 \mathrm{i} .
\end{array}
$$