AS CCEA Further Mathematics: Formula & Theorem Quick Reference | AS CCEA 进阶数学：公式定理速查手册

📚 AS CCEA Further Mathematics: Formula & Theorem Quick Reference | AS CCEA 进阶数学：公式定理速查手册

This quick-reference handbook brings together the essential formulas and theorems for the CCEA AS Further Mathematics course. Each section presents core results concisely, providing both English and Chinese explanations so you can revise efficiently.

本速查手册汇总了CCEA AS进阶数学课程必备的公式与定理。每节以中英对照简洁呈现核心结论，帮助高效复习。

1. Complex Numbers | 复数

A complex number can be expressed in Cartesian form as z = x + iy, where x and y are real and i² = −1.

复数可表示为笛卡儿形式 z = x + iy，其中 x, y 为实数，且 i² = −1。

The complex conjugate is z* = x − iy. The product z z* = x² + y² is always real and gives |z|².

共轭复数为 z* = x − iy。乘积 z z* = x² + y² 恒为实数，即为 |z|²。

Modulus: |z| = √(x² + y²). Argument: θ = arg(z) with tan θ = y/x, adjusted to the correct quadrant.

模：|z| = √(x² + y²)。辐角：θ = arg(z)，满足 tan θ = y/x，并需确定正确象限。

Euler’s formula: e^(iθ) = cos θ + i sin θ. De Moivre’s theorem: (cos θ + i sin θ)ⁿ = cos nθ + i