Ivan Shishkin, Birch Grove

Formule de Moivre

Definition / Other /

Showing the Français version because no English translation exists yet. Add that translation.

Français
FrançaisAdd translation
Formule de Moivre

Soit θ∈R\theta \in \mathbb{R}, n∈Nn \in \mathbb{N},
(cos⁡(θ)+isin⁡(θ))n=cos⁡(nθ)+isin⁡(nθ).\bigl(\cos(\theta)+i\sin(\theta)\bigr)^n = \cos(n\theta)+i\sin(n\theta).

Remarque
  • Il en découle que
    Re⁡((cos⁡θ+isin⁡θ)n)=cos⁡(nθ)\quad \Re\bigl( (\cos\theta+i\sin\theta)^n \bigr) = \cos(n\theta)et Im⁡((cos⁡θ+isin⁡θ)n)=sin⁡(nθ)\text{et }\Im\bigl( (\cos\theta+i\sin\theta)^n \bigr) = \sin(n\theta)
Problems using this concept (0)

No listed problems link to this concept yet.

Problems using this concept (spoiler) (0)

No listed problems use this concept as a spoiler yet.