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MATH / A sequence of complex numbers z₀,z₁,z₂,… is defined by the rule z_(n+1)=( iz_(n) )/((z)¯_(n)),where (z)¯_(n) is the complex conjugate of z_(n) and i²=−1. Suppose that |z₀|=1 and …

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problem

A sequence of complex numbers z0,z1,z2,…z_0,z_1,z_2,\ldots is defined by the rule zn+1=iznz¯n, z_{n+1}=\frac{\ iz_n\ }{\overline{z}_n}, where z¯n\overline{z}_n is the complex conjugate of znz_n and i2=−1i^2=-1. Suppose that |z0|=1|z_0|=1 and z2005=1z_{2005}=1. How many possible values are there for z0z_0?
Plain-text mathematical notation (without MathML)
A sequence of complex numbers z₀,z₁,z₂,… is defined by the rule z_(n+1)=( iz_(n) )/((z)¯_(n)),where (z)¯_(n) is the complex conjugate of z_(n) and i²=−1. Suppose that |z₀|=1 and z₂₀₀₅=1. How many possible values are there for z₀?
Original LaTeX notation
A sequence of complex numbers $z_0,z_1,z_2,\ldots$ is defined by the rule \[
z_{n+1}=\frac{\ iz_n\ }{\overline{z}_n},
\]where $\overline{z}_n$ is the complex conjugate of $z_n$ and $i^2=-1$. Suppose that $|z_0|=1$ and $z_{2005}=1$. How many possible values are there for $z_0$?

level

Level 4

type

Precalculus

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Source and history

task_id
a444368a-7983-576b-bbfe-6782b2beffcb
task_key
precalculus--test--a444368a-7983-576b-bbfe-6782b2beffcb
task_revision_id
1
config / split
precalculus / test

Official source

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