On the Nonmonotonicity of (Im(zn))

Bruce Reznick

doi:10.1006/jnth.1999.2394

On the Nonmonotonicity of (Im(zⁿ))

Bruce Reznick

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the sequence (Im(zⁿ)) is never monotone when z is a non-real complex number, and (Re(zⁿ)) is never monotone, unless z=re^iπθ, where θ=k/m for some odd m, and r is sufficiently large or sufficiently small. Similar results hold for the length of the projection of zⁿ onto any line through the origin.

Original language	English (US)
Pages (from-to)	144-148
Number of pages	5
Journal	Journal of Number Theory
Volume	78
Issue number	1
DOIs	https://doi.org/10.1006/jnth.1999.2394
State	Published - Sep 1999

ASJC Scopus subject areas

Algebra and Number Theory

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10.1006/jnth.1999.2394

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Cite this

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title = "On the Nonmonotonicity of (Im(zn))",

abstract = "We show that the sequence (Im(zn)) is never monotone when z is a non-real complex number, and (Re(zn)) is never monotone, unless z=reiπθ, where θ=k/m for some odd m, and r is sufficiently large or sufficiently small. Similar results hold for the length of the projection of zn onto any line through the origin.",

author = "Bruce Reznick",

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