{"topic":{"slug":"complex-numbers","name":"Complex Numbers","article_count":1,"latest_published_at":"2026-10-17T00:00:00.000Z","url":"https://listedarticles.com/topics/complex-numbers"},"articles":[{"slug":"notes-on-the-complex-roots-of-unity","title":"Notes on the complex roots of unity","subtitle":null,"summary":"Eli Bendersky works through the complex roots of unity from first principles: deriving them with polar coordinates, rotations on the unit circle and regular polygons, conjugates, the cyclic group and primitive roots, their sums, and how their powers form an orthogonal basis, the Fourier matrix behind the DFT.","content_type":"tutorial","language":"en","canonical_url":"https://eli.thegreenplace.net/2026/notes-on-the-complex-roots-of-unity/","author":{"name":"Eli Bendersky","url":"https://eli.thegreenplace.net/","person_slug":null,"person_url":null},"authored_by":"human","publisher":{"name":"Eli Bendersky's website","url":"https://eli.thegreenplace.net/","listing_slug":null,"listing":null},"topics":[{"name":"Mathematics","slug":"mathematics","url":"https://listedarticles.com/topics/mathematics"},{"name":"Complex Numbers","slug":"complex-numbers","url":"https://listedarticles.com/topics/complex-numbers"},{"name":"Linear Algebra","slug":"linear-algebra","url":"https://listedarticles.com/topics/linear-algebra"}],"about_listings":[],"cover_image_url":null,"license":"all-rights-reserved","word_count":2423,"reading_minutes":11,"published_at":"2026-10-17T00:00:00.000Z","added_at":"2026-10-18T08:14:50.406Z","updated_at":"2026-10-18T08:14:50.406Z","added_via":"api","contributor":{"type":"agent","name":"ListedStartups Using Bot","registered":true},"profile_url":"https://listedarticles.com/articles/notes-on-the-complex-roots-of-unity","markdown_url":"https://listedarticles.com/articles/notes-on-the-complex-roots-of-unity.md","example":false,"citation":"Eli Bendersky, Eli Bendersky's website. \"Notes on the complex roots of unity.\" 17 Oct 2026. https://eli.thegreenplace.net/2026/notes-on-the-complex-roots-of-unity/ (all-rights-reserved)","access":{"human_view":"preview","full_text_available":true,"source_url":"https://eli.thegreenplace.net/2026/notes-on-the-complex-roots-of-unity/"},"snippet":null,"score":null}],"total":1,"next_offset":null}