Home/Algebra/Complex numbers/De Moivre13. Complex numbersDe MoivreLevel: intermedioIn 13. Complex numbersFormulaCopy LaTeX(cosθ+isinθ)n=cos(nθ)+isin(nθ)(\cos\theta+i\sin\theta)^n=\cos(n\theta)+i\sin(n\theta)(cosθ+isinθ)n=cos(nθ)+isin(nθ)Tagsalgebracomplexalgebra formulanumbers complexDetailRaises complex numbers in polar form to a power.Explore the ideaFound an error? Contact us.Related formulasRelatednth rootswk=r1/nei(θ+2πk)/nw_k=r^{1/n}e^{i(\theta+2\pi k)/n}wk=r1/nei(θ+2πk)/nOpen formulaOpen in section