V2EX imaginary unit

Imaginary Unit

定义 Definition

虚数单位:复数中的基本单位,通常记作 i(工程与物理中也常用 j),定义为
\( i^2 = -1 \),等价于 \( i = \sqrt{-1} \)。它用来表示实数轴“垂直方向”的成分,从而构成复平面上的复数。

例句 Examples

The imaginary unit is defined so that \( i^2 = -1 \).
虚数单位的定义是使得 \( i^2 = -1 \)。

Using the imaginary unit, we can rewrite the solution as a complex number and analyze its magnitude and phase.
借助虚数单位,我们可以把解改写为复数,并分析它的模与相位。

发音 Pronunciation

/mdnri junt/

词源 Etymology

imaginary 源自拉丁语 imaginarius(“想象的、虚构的”),早期数学中用来描述“不属于实数范围”的量;unit 源自拉丁语 unus(“一”),表示“单位、基本量”。合起来的 imaginary unit 指复数体系中那一个“基本的虚数单位” \( i \)。

相关词 Related Words

文学与名著中的出现 Literary Works

  • A Course of Pure Mathematics G. H. Hardy(讲解复数与 \(i\) 的基础用法)
  • Complex Analysis Lars Ahlfors(经典复分析教材,频繁使用虚数单位)
  • Visual Complex Analysis Tristan Needham(以几何方式解释 \(i\) 与复平面)
  • Introduction to Complex Analysis H. A. Priestley(入门复分析,系统介绍 \(i\))
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