Year 13 OCR Further Maths: Vocabulary & Terminology Quick Reference | Year 13 OCR 进阶数学：词汇术语速记指南

📚 Year 13 OCR Further Maths: Vocabulary & Terminology Quick Reference | Year 13 OCR 进阶数学：词汇术语速记指南

This guide presents essential vocabulary and terminology for the OCR Year 13 Further Mathematics syllabus. Each term is explained with a concise definition and a memory aid to help you revise rapidly. The topics span core pure, statistics, mechanics and discrete mathematics.

本指南列出了OCR Year 13进阶数学大纲中的核心词汇和术语。每个术语都配有简明定义和速记提示，帮助你快速复习。内容涵盖纯数核心、统计、力学及离散数学。

1. Complex Numbers | 复数

Imaginary unit i – defined as i² = –1, enabling square roots of negative numbers.

虚数单位 i – 定义 i² = –1，可求负数的平方根。

Complex number z = x + iy, where x is the real part Re(z) and y is the imaginary part Im(z).

复数 z = x + iy，其中 x 为实部 Re(z)，y 为虚部 Im(z)。

Complex conjugate of z = x + iy is z* = x – iy. Note: z z* = |z|² is always real.

共轭复数 z = x + iy 的共轭为 z* = x – iy。注意 z z* = |z|² 恒为实数。

Modulus |z| = √(x² + y²) – the distance from the origin in the Argand diagram.

模 |z| = √(x² + y²) – 在阿尔冈图中表示到原点的距离。

Argument arg(z) = θ, where tan θ = y/x. The principal argument lies in (–π, π].

辐角 arg(z) = θ，tan θ = y/x。主辐角在 (–π, π] 范围内。

Polar form: z = r(cos θ + i sin θ) = r e^(iθ). A great shortcut for multiplication and division.

极坐标形式: z = r(cos θ + i sin θ) = r e^(iθ)。用于乘除运算的便捷形式。

De Moivre’s theorem: (cos θ + i sin θ)^n = cos(nθ) + i sin(nθ). Powers and roots made easy.

棣莫弗定理: (cos θ + i sin θ)^n = cos(nθ) + i sin(nθ)。简便计算幂与根。

2. Matrices and Linear Transformations | 矩阵与线性变换

Order of a matrix: an m × n matrix has m rows and n columns.

矩阵的阶: m × n 矩阵有 m 行 n 列。

Identity matrix I: square matrix with 1s on the leading diagonal and 0s elsewhere. AI = IA

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