📚 AS CCEA Further Mathematics: Glossary & Terminology Quick Study Guide | AS CCEA 进阶数学：词汇术语速记指南
Mastering the precise vocabulary of AS Further Mathematics is just as important as learning the techniques. This guide clarifies the key terms and notations you will encounter in CCEA's AS Further Pure and applied modules, helping you read questions accurately and express solutions confidently.
精通 AS 进阶数学的精确词汇与掌握解题技巧同等重要。本指南将厘清 CCEA AS 进阶纯数及应用模块中常见的核心术语与记号，帮助你准确审题、自信作答。
1. Complex Numbers and Imaginary Unit | 复数与虚数单位
nit i satisfies i² = −1. A complex number is any number of the form z = x + iy, where x, y ∈ ℝ sed for division and to prove properties of real numbers arising from complex expressions.
虚数单位 i 满足 i² = −1。复数指任何可以写成 z = x + iy 形式的数，其中 x, y 为实数。实部 Re(z) = x，虚部 Im(z) = y。z 的共轭复数记作 z* = x − iy。共轭常用于复数除法以及证明由复数表达式衍生的实部性质。
The modulus of z is the distance from the origin on an Argand diagram: |z| = √x² + y² ve real axis, usually given in radians. The polar form is z = r(cos θ + i sin θ), with r = |z|. De Moivre' n(nθ) for any integer n, and is essential for finding powers and roots of complex numbers.
模 |z| 是阿冈图上从原点到该点的距离：|z| = √x² + y²。辐角 arg(z) 是从正实轴开始逆时针旋转的角度 θ，通常以弧度表示。极坐标形式为 z = r(cos θ + i sin θ)，其中 r = |z|。棣莫弗定理指出，对任意整数 n 有 (cos θ + i sin θ)ⁿ = cos(nθ) + i sin(nθ)，这是求复数幂和根的核心工具。
2. Matrices | 矩阵
s). The identity matrix I has 1 on the leading diagonal and 0 elsewhere. The zero matrix O has every entry 0. The transpose of a matrix A, written AT, is formed by interchanging rows and columns. A matrix is symmetric if AT = A.
矩阵是数的矩形阵列；其阶数为 m × n（行数×列数）。单位矩阵 I 的主对角线元素为 1，其余元素为 0。零矩阵 O 的所有元素均为 0。矩阵 A 的转置 AT 通过交换行与列得到。若 AT = A，则 A 为对称矩阵。
lar if det(A) = 0, meaning it has no inverse. The inverse matrix A⁻¹ satisfies AA⁻¹ = A⁻¹A = I. Only non-singular matrices have inverses. For a 2 × 2 matrix, A⁻¹ = (1/det A) [[d, −b], [−c, a]]. Orthogonal matrices satisfy A⁻¹ = AT, preserving lengths and angles.
2 × 2 矩阵 A = [[a, b], [c, d]] 的行列式为 det(A) = ad − bc。3 × 3 行列式通过余子式展开求得。若 det(A) = 0，该矩阵为奇异矩阵，不存在逆矩阵。逆矩阵 A⁻¹ 满足 AA⁻¹ = A⁻¹A = I。只有非奇异矩阵才有逆。2 × 2 逆矩阵公式为 A⁻¹ = (1/det A) [[d, −b], [−c, a]]。正交矩阵满足 A⁻¹ = AT，能保持长度和角度不变。
3. Vectors in Three Dimensions | 三维向量
e expressed in component form v = a i + b j + c k, or as a column vector. The magnitude is |v| = √a² + b² + c². A unit vector has magnitude 1; the unit vector in the direction of v is v̂ = v / |v|.
三维向量可用分量形式 v = a i + b j + c k 或列向量表示。模长为 |v| = √a² + b² + c²。单位向量模长为 1；沿 v 方向的单位向量为 v̂ = v / |v|。
The scalar (or dot) product is u · v = a₁a₂ + b₁b₂ + c₁c₂ = |u||v| The vector (or cross) product u × v yields a vector perpendicular to both, with magnitude |u||v| rm as r = a + λ d, where a is a position vector to a point on the line and d is the direction vector.
数量积（点积）为 u · v = a₁a₂ + b₁b₂ + c₁c₂ = |u||v| cos θ。当两向量垂直时点积为零。向量积（叉积）u ×
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