Square Roots of a Complex Number: Visualizing Two Roots in the Complex Plane

This GeoGebra worksheet visualizes the two square roots of a complex number N in the complex plane. It demonstrates the geometric interpretation of complex square roots using polar form and De Moivre's theorem: the modulus of each root is the square root of the original modulus, and the arguments are half the original argument (differing by π). The construction uses complex number objects (N, A, p) to define the input, computes the roots via polar conversion, marks the roots as points A₀ and A₁, and includes a slider k to adjust parameters. Text objects (text1–text5) explain the steps. This resource is ideal for high school or early college students learning complex numbers, and for teachers demonstrating the symmetry of roots in the complex plane.