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Everything about Root of unity

Number with an integer power equal to 1

In mathematics, a root of unity is any complex number that yields 1 when raised to some positive integer power n. Roots of unity are used in many branches of mathematics, and are especially important in number theory, the theory of group characters, and the discrete Fourier transform. It is occasionally called a de Moivre number after French mathematician Abraham de Moivre. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Root of unityA 5-minute orientation
  2. Skim a recent paper: The root microbiome: Community assembly and its contributions to plant fitnessInfluential work since 2022
  3. Pick up a classic book: Can't stop, won't stopThe most-reprinted book on the subject
  4. Read the landmark paper: Dynamic root exudate chemistry and microbial substrate preferences drive patterns in rhizosphere microbial community assemblyCited 2,410 times
  5. Go sideways: Cyclotomic polynomialA closely related topic
  6. Go sideways: Minimal polynomial of 2cos(2pi/n)A closely related topic

📖 Definitions

Noun An element of a given field (especially, a complex number) x such that for some positive integer n, x = 1.

🗂️ The subject at a glance

  1. General definition
  2. Elementary properties
  3. Group properties
  4. Trigonometric expression
  5. Algebraic expression
  6. Periodicity
  7. Summation
  8. Orthogonality
  9. Cyclotomic polynomials
  10. Cyclic groups
  11. Cyclotomic fields
  12. Relation to quadratic integers

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics