div_ofNat — Mathlib

English

For z ∈ ℂ and n ∈ ℕ with n ≥ 2, z / ofNat(n) = (Re(z))/ofNat(n) + i (Im(z))/ofNat(n).

Русский

Для z ∈ ℂ и n ∈ ℕ с n ≥ 2, z / ofNat(n) = (Re(z))/ofNat(n) + i (Im(z))/ofNat(n).

LaTeX

$$$\\dfrac{z}{\\operatorname{ofNat}(n)} = \\dfrac{\\operatorname{Re}(z)}{\\operatorname{ofNat}(n)} + i\\,\\dfrac{\\operatorname{Im}(z)}{\\operatorname{ofNat}(n)}$$$

Lean4

theorem div_ofNat (z : ℂ) (n : ℕ) [n.AtLeastTwo] : z / ofNat(n) = ⟨z.re / ofNat(n), z.im / ofNat(n)⟩ :=
  div_natCast z n

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