📚 A-Level Further Maths Unit 5 June 2022: Key Concepts Explained | A-Level 进阶数学 Unit 5 2022年6月考卷知识点精讲
The June 2022 Unit 5 paper for A-Level Further Mathematics tested a wide range of pure topics, from complex numbers and matrices to differential equations and polar coordinates. This article breaks down the key concepts every student must master, offering clear explanations and examples directly linked to the exam style.
2022年6月的A-Level进阶数学Unit 5试卷考查了从复数、矩阵到微分方程与极坐标的广泛纯数主题。本文将逐一拆解每位考生必须掌握的核心概念，提供紧扣真题风格的清晰讲解与示例。
1. Complex Numbers – De Moivre’s Theorem | 复数与棣莫弗定理
De Moivre’s theorem is a cornerstone for handling powers and roots of complex numbers. It states that for any complex number z = r(cosθ + i sinθ) and integer n: zⁿ = rⁿ (cos nθ + i sin nθ). In the June 2022 exam, candidates were expected to apply this to evaluate expressions like (√3 + i)⁵ or to find the cube roots of a given complex number.
棣莫弗定理是处理复数幂与根的核心工具。定理表明，对任意复数 z = r(cosθ + i sinθ) 与整数 n 有 zⁿ = rⁿ (cos nθ + i sin nθ)。
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