Home/Algebra/Complex numbers/nth roots13. Complex numbersnth rootsLevel: intermedioIn 13. Complex numbersFormulaCopy LaTeXwk=r1/nei(θ+2πk)/nw_k=r^{1/n}e^{i(\theta+2\pi k)/n}wk=r1/nei(θ+2πk)/nTagsalgebracomplexalgebra formulanumbers complexDetailThe roots are distributed uniformly on a circle.Explore the ideaFound an error? Contact us.Related formulasRelatedDe Moivre(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)Open formulaOpen in sectionRelatedFactorization by rootsP(x)=an∏k=1n(x−rk)P(x)=a_n\prod_{k=1}^{n}(x-r_k)P(x)=ank=1∏n(x−rk)Open formulaOpen in section