Lean-Workbook Plus 33584: Exponential inequality

Proved

WorkbookRestored.plus_33584

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For every positive natural number $n$ , $(\exp(2\pi i/n))^n-1=0$ .

Source: Lean-Workbook row lean_workbook_plus_33584 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble

import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
open Real

Formal statement

theorem WorkbookRestored.plus_33584  (n : ℕ)
  (h₀ : 0 < n) :
  ((Complex.exp (2 * π * Complex.I / n))^n - 1) = 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_33584; immutable original Prove2Me node a59c0200-4bc1-415b-95e0-437da02e407a

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