Prove2Me

`BookProof.ChapterSternGerlach.dft_geom_sum_zero` (n : ℕ) (w : ℂ) (hw : w ≠ 1) (hwn : w ^ n = 1) : ∑ i ∈ Finset.range n, w ^ i = 0

Proved
BookProof.ChapterSternGerlach.dft_geom_sum_zero

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSternGerlach.

BookProof.ChapterSternGerlach.dft_geom_sum_zero (n : ℕ) (w : ℂ) (hw : w ≠ 1) (hwn : w ^ n = 1) : ∑ i ∈ Finset.range n, w ^ i = 0

Formalization note: Lean 4 identifier BookProof.ChapterSternGerlach.dft_geom_sum_zero.

Preamble
-- Generated from ChapterSternGerlach.lean — theorem BookProof.ChapterSternGerlach.dft_geom_sum_zero
import Mathlib
import Definitions.Def_ChapterSternGerlach
open BookProof.ChapterSternGerlach



open Complex Matrix Finset
Formal statement
theorem BookProof.ChapterSternGerlach.dft_geom_sum_zero (n : ℕ) (w : ℂ) (hw : w ≠ 1) (hwn : w ^ n = 1) :
    ∑ i ∈ Finset.range n, w ^ i = 0 := by sorry

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