Further Core Pure 1 Revision Guide: Key Methods and Exam Tips | 进阶核心纯数1复习指南：关键方法与应试技巧

📚 Further Core Pure 1 Revision Guide: Key Methods and Exam Tips | 进阶核心纯数1复习指南：关键方法与应试技巧

Further Core Pure 1 is the foundation module for A-level Further Mathematics. It brings together complex numbers, matrices, series, proof, polar coordinates, hyperbolic functions and differential equations. This revision guide explains the main methods in clear steps and highlights common exam traps.

进阶核心纯数1是A-level进阶数学的基础模块，综合考查复数、矩阵、级数、证明、极坐标、双曲函数和微分方程。本复习指南以清晰步骤讲解主要方法，并强调常见考试陷阱。

1. Complex Numbers: Forms and Operations | 复数：表示形式与运算

A complex number is written as z = a + bi, where a and b are real numbers and i² = -1. The real part is a, and the imaginary part is b. Addition and subtraction follow standard algebra, while multiplication uses i² = -1 to simplify.

复数写作 z = a + bi，其中 a 和 b 是实数且 i² = -1。实部是 a，虚部是 b。加减法按常规代数运算，乘法利用 i² = -1 进行化简。

The conjugate of z = a + bi is z* = a – bi. The modulus is |z| = √(a² + b²), which gives the distance from the origin in the Argand diagram. Division is done by multiplying the numerator and denominator by the conjugate of the denominator.

z = a + bi 的共轭复数是 z* = a – bi。模为 |z| = √(a²

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