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The principal root of one has unit norm

Proved
WorkbookRestored.plus_727

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

lean-workbookrestored-importssource-checked

For every natural n≠0n\ne0n=0, the principal complex power satisfies ∣11/n∣=1|1^{1/n}|=1∣11/n∣=1.

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_727 (Apache-2.0).

Preamble
import Mathlib.Analysis.SpecialFunctions.Pow.Complex
open Complex
Formal statement
theorem WorkbookRestored.plus_727 (n : ℕ) (hn : n ≠ 0) : ‖(1 : ℂ) ^ (1 / n : ℂ)‖ = 1   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_727; original Prove2Me node f21e6850-1704-49b6-a569-e6ae650a1611; Apache-2.0

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