complex unit circle

set of complex numbers whose absolute value is equal 1; Lie group of complex numbers of unit modulus; topologically a circle
Thing set_of_numbers Q105356493
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complex unit circle

Summary

complex unit circle is a set of numbers[1]. It draws 84 Wikipedia views per month (set_of_numbers category, ranking #3 of 5).[2]

Key Facts

  • complex unit circle's image is recorded as Circle as Lie group.svg[3].
  • complex unit circle's instance of is recorded as set of numbers[4].
  • complex unit circle's instance of is recorded as unitary group[5].
  • complex unit circle's instance of is recorded as special orthogonal group[6].
  • complex unit circle's instance of is recorded as spin group[7].
  • complex unit circle's instance of is recorded as divisible group[8].
  • complex unit circle's instance of is recorded as Abelian Lie group[9].
  • complex unit circle's instance of is recorded as compact Lie group[10].
  • complex unit circle's followed by is recorded as rotation group SO(3)[11].
  • complex unit circle's subclass of is recorded as unit circle[12].
  • complex unit circle's subclass of is recorded as complex number[13].
  • complex unit circle's part of is recorded as set of complex numbers without zero[14].
  • complex unit circle's Commons category is recorded as Complex unit circle[15].
  • complex unit circle's has part is recorded as complex unit[16].
  • complex unit circle's Freebase ID is recorded as /m/02jrlh[17].
  • complex unit circle's has characteristic is recorded as magnitude of a complex number[18].
  • complex unit circle's defining formula is recorded as {z \colon \vert z \vert = 1} = {z \colon z = e ^ {i\theta} = \mathrm{cis} (\theta) = \cos\theta + i\sin\theta \colon \theta \in \mathbb{R} }[19].
  • complex unit circle's studied by is recorded as Lie theory[20].
  • complex unit circle's Quora topic ID is recorded as Circle-Group[21].
  • complex unit circle's nLab ID is recorded as circle group[22].
  • complex unit circle's maintained by WikiProject is recorded as WikiProject Mathematics[23].
  • complex unit circle's Microsoft Academic ID is recorded as 49642718[24].
  • complex unit circle's in defining formula is recorded as z[25].
  • complex unit circle's in defining formula is recorded as { . . }[26].
  • complex unit circle's in defining formula is recorded as i[27].

Why It Matters

complex unit circle draws 84 Wikipedia views per month (set_of_numbers category, ranking #3 of 5).[2] It has Wikipedia articles in 15 language editions, a strong signal of global cultural recognition.[28] It is known by 18 alternative names across languages and contexts.[29]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . Freebase Data Dumps. wikidata.org.
  16. [18] . wikidata.org.
  17. [19] . wikidata.org.
  18. [20] . wikidata.org.
  19. [21] . Quora. wikidata.org.
  20. [22] . wikidata.org.
  21. [23] . wikidata.org.
  22. [24] . wikidata.org.
  23. [25] . wikidata.org.
  24. [26] . wikidata.org.
  25. [27] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [28] . Wikidata sitelinks. wikidata.org.
  3. [29] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). complex unit circle. Retrieved May 3, 2026, from https://4ort.xyz/entity/complex-unit-circle
MLA “complex unit circle.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/complex-unit-circle.
BibTeX @misc{4ortxyz_complex-unit-circle_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{complex unit circle}}, year = {2026}, url = {https://4ort.xyz/entity/complex-unit-circle}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): complex unit circle — https://4ort.xyz/entity/complex-unit-circle (retrieved 2026-05-03)

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