On the Nonmonotonicity of (Im(zn))

Research output: Contribution to journalArticlepeer-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=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.

Original languageEnglish (US)
Pages (from-to)144-148
Number of pages5
JournalJournal of Number Theory
Volume78
Issue number1
DOIs
StatePublished - Sep 1999

ASJC Scopus subject areas

  • Algebra and Number Theory

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