V2EX complex plane

Complex Plane

释义 Definition

复平面:在数学中,用来表示复数的二维平面。通常把复数 \(z=a+bi\) 表示为平面上的点 \((a,b)\):横轴为实轴(real axis),纵轴为虚轴(imaginary axis)。

发音 Pronunciation (IPA)

/kmpleks plen/

例句 Examples

The complex plane helps us visualize complex numbers.
复平面帮助我们把复数形象地表示出来。

By mapping each value onto the complex plane, we can see how the function behaves near its singularities.
把每个取值映射到复平面上,我们就能看出函数在其奇点附近的行为。

词源 Etymology

complex plane 是由 complex(复数的) + plane(平面) 组成的数学术语。这里的 complex 源自拉丁语 complexus,有“交织、组成整体”的意思;在数学里引申为“由实部与虚部共同构成”的复数系统。plane 源自拉丁语 planus,意为“平坦的”,引申为“平面”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Visual Complex Analysis(Tristan Needham):在几何直观的讲解中大量使用复平面来解释复变函数与映射。
  • Complex Analysis(Elias M. Stein & Rami Shakarchi):以复平面为基础讨论解析函数、积分与留数等核心概念。
  • Ahlfors’ Complex Analysis(Lars V. Ahlfors):经典复分析教材,复平面与其几何结构贯穿全书。
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