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Complex numbers › Complex arithmetic › Dividing complex numbers

Term of a complex recurrence

High school · ●●●○○ 50 pts

The sequence of complex numbers {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,…n=1,2,\ldots. Write z2015=a+biz_{2015}=a+bi, where aa and bb are real numbers. Find aa and bb.

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complex conjugaterecurrence relations