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Complex sequence with conjugate recurrence

High school · ●●●○○ 50 pts

The complex number sequence {zn}\{z_n\} satisfies z1=1z_1=1 and zn+1=zn‾+1+niz_{n+1}=\overline{z_n}+1+ni for n=1,2,3,…n=1,2,3,\dots, where ii is the imaginary unit and zn‾\overline{z_n} is the conjugate of znz_n. Find the real part and the imaginary part of z2015z_{2015}.

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