Home/Algebra/Complex numbers/Euler's formula13. Complex numbersEuler's formulaLevel: intermedioIn 13. Complex numbersFormulaCopy LaTeXeiθ=cosθ+isinθe^{i\theta}=\cos\theta+i\sin\thetaeiθ=cosθ+isinθTagsalgebracomplexalgebra formulanumbers complexDetailConnects complex exponentials with trigonometry.Explore the ideaFound an error? Contact us.Related formulasRelatedPolar and exponential formz=r(cosθ+isinθ)=reiθz=r(\cos\theta+i\sin\theta)=re^{i\theta}z=r(cosθ+isinθ)=reiθOpen formulaOpen in sectionRelatedDe 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 section