Edexcel•A-Level•Further Maths
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Complex Numbers (Further)
De Moivre's theorem, exponential form, and nth roots
Practice 15 subtopics in Complex Numbers (Further). All questions match the Edexcel A-Level specification.
About Complex Numbers (Further)
Complex Numbers (Further) is a key topic in the Edexcel A-Level Further Mathsspecification. This topic covers de moivre's theorem, exponential form, and nth roots.
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Euler's formula: e^(iθ) = cos θ + i sin θExponential form: z = re^(iθ)Multiplication in exponential formDivision in exponential formDe Moivre's theorem: (cos θ + i sin θ)ⁿ = cos(nθ) + i sin(nθ)Proof by inductionApplications to trigonometric identitiesExpressing cos(nθ) in terms of cos θExpressing sin(nθ) in terms of sin θnth roots of unityRoots of z^n = wGeometric properties of rootsSum of nth roots of unityTransformations w = f(z)Loci under transformations
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Start with Euler's formula: e^(iθ) = cos θ + i sin θ