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单词 Complex conjugation
释义

Complex conjugation

中文百科

共轭复数 Complex conjugate

(重定向自Complex conjugation)

在数学中,复数的复共轭(常简称共轭)是对虚部**的运算,因此一个复数

 z=a+ib \, \quad (a, b \in \R)

的复共轭是

\overline{z} = a - ib.\,

举例明之:

\overline{(3-2i)} = 3 + 2i
\overline{7}=7

在复数的极坐标表法下,复共轭写成

\overline{r e^{i\theta}} = r e^{-i\theta}

这点可以透过欧拉公式验证

将复数理解为复平面,则复共轭无非是对实轴的反射。复数z的复共轭有时也表为z^*

英语百科

Complex conjugate 共轭复数

(重定向自Complex conjugation)
Geometric representation of z and its conjugate z̅ in the complex plane. The complex conjugate is found by reflecting z across the real axis.

In mathematics, the complex conjugate of a complex number is the number with equal real part and imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of 3 + 4i is 3 4i.

In polar form, the conjugate of \rho e^{i \phi} is \rho e^{-i \phi}. This can be shown using Euler's formula.

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