AQA•A-Level•Further Maths
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Complex Numbers
The complex number system, Argand diagrams, and De Moivre's theorem
Practice 27 subtopics in Complex Numbers. All questions match the AQA A-Level specification.
About Complex Numbers
Complex Numbers is a key topic in the AQA A-Level Further Mathsspecification. This topic covers the complex number system, argand diagrams, and de moivre's theorem.
Master all 27 subtopics below with unlimited AI-generated questions. Each subtopic page includes sample questions and the ability to generate unlimited practice questions with detailed solutions.
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Definition of i: i^2 = -1Real and imaginary partsComplex conjugatesAddition and subtractionMultiplication of complex numbersDivision using conjugatesSolving quadratics with complex rootsComplex conjugate root theoremSolving polynomials with complex rootsFinding all roots of polynomialsArgand diagram representationModulus of complex numbers |z|Argument of complex numbers arg(z)Modulus-argument form: r(cos θ + i sin θ)Exponential form: re^(iθ)Geometric interpretation of operationsDe Moivre's theorem: (cos θ + i sin θ)^nProving trigonometric identitiesFinding cos(nθ) and sin(nθ)nth roots of unitynth roots of complex numbersRoots on Argand diagramLocus |z - a| = r (circle)Locus |z - a| = |z - b| (perpendicular bisector)Locus arg(z - a) = θ (half-line)Regions in the complex planeTransformations w = z + a, w = kz, w = z*
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