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Omni-MATH / Given complex number z, define sequence z₀,z₁,z₂,… as z₀=z and z_(n+1)=2z_(n)²+2z_(n) for n≥0. Given that z₁₀=2017, find the minimum possible value of |z|.

Problem

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problem

Given complex number zz, define sequence z0,z1,z2,…z_{0}, z_{1}, z_{2}, \ldots as z0=zz_{0}=z and zn+1=2zn2+2znz_{n+1}=2 z_{n}^{2}+2 z_{n} for n≥0n \geq 0. Given that z10=2017z_{10}=2017, find the minimum possible value of |z||z|.
Plain-text mathematical notation (without MathML)
Given complex number z, define sequence z₀,z₁,z₂,… as z₀=z and z_(n+1)=2z_(n)²+2z_(n) for n≥0. Given that z₁₀=2017, find the minimum possible value of |z|.
Original LaTeX notation
Given complex number $z$, define sequence $z_{0}, z_{1}, z_{2}, \ldots$ as $z_{0}=z$ and $z_{n+1}=2 z_{n}^{2}+2 z_{n}$ for $n \geq 0$. Given that $z_{10}=2017$, find the minimum possible value of $|z|$.

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Source and history

task_id
9b3541e1-1f0f-5213-a317-1abe2e34f041
task_key
test--9b3541e1-1f0f-5213-a317-1abe2e34f041
task_revision_id
1
config / split
/ test

Official source

initial import