IGCSE CCEA Maths: Complex Numbers | IGCSE CCEA 数学：复数考点精讲

📚 IGCSE CCEA Maths: Complex Numbers | IGCSE CCEA 数学：复数考点精讲

Complex numbers are a vital extension of the real number system, introduced in CCEA IGCSE Mathematics to solve equations that have no real solutions. Understanding complex numbers opens the door to advanced topics in algebra, calculus, and engineering. This revision guide covers all key points you need to master for the CCEA IGCSE exam.

复数是实数系统的重要扩展，CCEA IGCSE 数学引入复数用于求解无实数解的方程。理解复数将为代数、微积分和工程学等高等话题打下基础。本复习指南涵盖CCEA IGCSE 考试所需掌握的所有要点。

1. Introduction to Complex Numbers | 复数入门

When you solve a quadratic equation such as x² + 1 = 0, you find that x² = −1. In the real number system, there is no real number whose square is negative. To handle such situations, mathematicians introduced the imaginary unit i, defined by i² = −1. Complex numbers are numbers of the form a + bi, where a and b are real numbers.

当你求解如 x² + 1 = 0 的二次方程时，会得到 x² = −1。在实数系统中，没有任何实数的平方是负数。为了处理这种情况，数学家引入了虚数单位 i，定义为 i² = −1。复数就是形如 a + bi 的数，其中 a 和 b 是实数。

A complex number combines a real part and an imaginary part. For example, 2 + 3i has real part 2 and imaginary part 3 (note that the imaginary part is the coefficient of i, not 3i). Complex numbers allow us to extend arithmetic and algebra seamlessly.

复数由一个实部和一个虚部组成。例如，2 + 3i 的实部是 2，虚部是 3（注意虚部是 i 的系数，而不是 3i）。复数让我们能够无缝地扩展算术和代数运算。

i² = −1

2. The Imaginary Unit i | 虚数单位 i

The imaginary unit i is defined such that

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