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单词 Argument of a complex number
释义

Argument of a complex number

中文百科

幅角 Argument (complex analysis)

（重定向自Argument of a complex number）
复数幅角的直观示意图

数学中，复数的幅角是指复数在复平面上对应的矢量和正向实数轴所成的有向角。复数的幅角值可以是一切实数，但由于相差360°（即弧度角2\pi）的幅角在实际应用中没有差别，所以定义复数的幅角主值为幅角模360°（即2\pi）后的余数，定义取值范围在0°到360°（即2\pi）之间。复数的幅角是复数的重要性质，在不少理论中都有重要作用。

英语百科

Argument (complex analysis) 幅角

（重定向自Argument of a complex number）
Figure 1. This Argand diagram represents the complex numbers lying on a plane. For each point on the plane, arg is the function which returns the angle φ.
Figure 3. Two choices for the argument φ
Figure 4. The principal value Arg of the blue point at 1 + i is π/4. The red line here is the branch cut and corresponds to the two red lines in figure 2 seen vertically above each other).
Figure 2. The arguments of the complex plane are plotted vertically. arg measures the angle of points, shown by the fact that the outward radial lines, which have constant angle to the real axis, lie on the surface. The layered structure shows that each point has infinitely many arguments, each one corresponding an intersection between a vertical line through the point and the sheet. The red hatching indicates the surface corresponding to the principal value. See larger version.

In mathematics, arg is a function operating on complex numbers (visualized in a complex plane). It gives the angle between the positive real axis to the line joining the point to the origin, shown as φ in figure 1, known as an argument of the point.
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