Angular Inequalities on an Argand Diagram: β ≤ arg(z−a) ≤ α

This example demonstrates how to visualize, on an Argand diagram, the set of complex numbers z for which the argument arg(z−a) lies between two bounds β and α. It builds a geometric region (an angular sector) whose rays form the inequality’s boundaries, making the meaning of argument constraints immediately visible. The core math concepts are complex numbers and their argument (arg), angle-based inequality interpretation on the complex plane relative to a reference point a, and geometric construction of solution sets. Construction-wise, the GeoGebra commands extracted from the provided summary include Rotate, Ray, Point, If (to express conditional behavior), Segment, Angle, Polygon, and CircleSector to create boundary rays, measure/label the angles, and generate the sector region. Key objects include the parameters α and β, the base point a, and several labeled points/angle quantities (e.g., θ, γ) used to display and control the construction. Suitable for high school to early undergraduate learning, especially for teaching the geometric meaning of arg, graphing solution regions for inequalities, and integrating complex numbers with coordinate geometry and interactive visualization.