A-Level WJEC Mathematics: Complex Numbers – Key Points Explained | 复数 考点精讲

📚 A-Level WJEC Mathematics: Complex Numbers – Key Points Explained | 复数 考点精讲

Complex numbers are a fundamental extension of the real number system, essential for solving equations where square roots of negative numbers appear. In the WJEC A-Level Mathematics syllabus, you are required to understand the algebra of complex numbers, their geometric representation on the Argand diagram, and the powerful De Moivre’s theorem for powers and roots. This article breaks down every key topic into clear, exam-focused explanations.

复数是实数系的基本扩展，对于求解涉及负数平方根的方程至关重要。在WJEC A-Level数学教学大纲中，你需要理解复数的代数运算、它们在阿尔甘特图上的几何表示以及用于幂和根的棣莫弗定理。本文将以清晰、针对考试的方式分解每个重要主题。

1. Introduction to Complex Numbers | 复数简介

The imaginary unit i is defined by the property i² = −1. A complex number z can be written as z = x + iy, where x and y are real numbers. The real part is denoted Re(z) = x, and the imaginary part is Im(z) = y. The set of all complex numbers is denoted ℂ.

虚数单位 i 由性质 i² = −1 定义。复数 z 可以写成 z = x + iy，其中 x 和 y 是实数。实部记为 Re(z) = x，虚部

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