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Complex recursive sequence z_2021

2050SpecialistComplex NumbersSequences & Series

China Mathematical Competition

Let complex sequence $\{z_n\}$ satisfy $$ z_1 = \frac{\sqrt{3}}{2}, \quad z_{n+1} = \overline{z_n}(1 + z_n i) \quad (n = 1, 2, \dots), $$ where $i$ is the imaginary unit. Find the value of $z_{2021}$.
0 students attempted0% solvedRating 2050

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