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In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg (z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in Figure 1.

2017年11月29日 · Start by constructing rays representing arguments of 0 0 (horizontal ray stretching to the right to infinity) and π 4 π 4 (a ray bisecting the first quadrant stretching upward and rightward to infinity). The blue area in between (strictly excluding the two rays themselves) represents the locus of points satisfying 0 <arg(w) <π 4 0 <arg (w) <π 4.

$\begingroup$ Part D is the set of $z\in\mathbb{C}$ for which $|z|^2=(arg \ z)^2 \ and \ \ 0 \le arg \ z < 2 \pi$. These $z$-values all have $|z|<2\pi$, so your graph should not spiral outward forever. $\endgroup$

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2023年7月23日 · This is easiest to see geometrically: the complex number $z-a$ can be thought of as representing the vector that joins $A$ to $Z$, where $A$ and $Z$ are the points represented by the complex numbers $a$ and $z$. Then $\arg(z-a)$ is "the angle from the positive $x$-direction to the direction of the vector represented by $z-a$" and your locus is ...

表达式：arg (z − z1) = θ. 解释：arg符号代表角的意思，z- z1代表z和另外一点的连线，也就是两点连线成某一个角度，是一条以z1为出发点，和水平方向成θ角的射线。

2020年8月5日 · So, the argument of a complex number is essentially just the angle the number makes with regards to the positive real axis: notice a negative angle means we go round clockwise, whereas a positive angle means we go round anti-clockwise. Now, z − 3 essentially means "take the complex number z, and then go left three units".