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Arithmetic-geometric series in complex z

High school · ●●○○○ 20 pts

Let z=1−2iz=1-2i. Find the real part and the imaginary part of 1z+2z2+3z3+⋯\frac{1}{z}+\frac{2}{z^{2}}+\frac{3}{z^{3}}+\cdots.

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arithmetic-geometric seriesinfinite series