Visualizing the N-th Root of a Complex Number via cis Form

This example demonstrates how to compute and visualize the n-th roots of a complex number z=a+bi on the complex plane using polar form. It focuses on the key ideas of complex numbers: modulus and argument, the multi-valued nature of roots, and expressing results with the cis (cos+ i sin) representation. The construction uses GeoGebra input and text/formatting commands to calculate parameters and display them clearly. From the provided construction summary: Textfield/InputBox objects gather parameters n and the real/imaginary parts (a, b); an If statement governs conditional root handling (e.g., branch selection or validity checks); intermediate complex quantities (z1), root magnitude (rRoot, r_{z1}), and angle (argm, angAdd, argR) are computed; FormulaText is used to render equations such as z= a+bi and each root candidate like A1= rRoot cis(angle). The resulting points A1…A8 illustrate multiple roots/branches. Suitable for high school to early university students learning complex analysis concepts visually, and for graphing/parameter exploration in mathematics classes.