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MATH / Let F(z)=(z+i)/(z−i) for all complex numbers znot= i, and let z_(n)=F(z_(n−1)) for all positive integers n. Given that z₀=(1)/(137)+i, find z₂₀₀₂.

Problem

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problem

Let F(z)=z+iz−iF(z)=\frac{z+i}{z-i} for all complex numbers $z\not= i,$ and let zn=F(zn−1)z_n=F(z_{n-1}) for all positive integers n.n. Given that z0=1137+i,z_0=\frac 1{137}+i, find z2002.z_{2002}.
Plain-text mathematical notation (without MathML)
Let F(z)=(z+i)/(z−i) for all complex numbers $z\not= i,$ and let z_(n)=F(z_(n−1)) for all positive integers n. Given that z₀=(1)/(137)+i, find z₂₀₀₂.
Original LaTeX notation
Let $F(z)=\frac{z+i}{z-i}$ for all complex numbers $z\not= i,$ and let $z_n=F(z_{n-1})$ for all positive integers $n.$ Given that $z_0=\frac 1{137}+i,$ find $z_{2002}.$

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
cfae6ce3-2cdd-54f8-b12d-4c8b75d3a1fa
task_key
intermediate~5falgebra--test--cfae6ce3-2cdd-54f8-b12d-4c8b75d3a1fa
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import