Real Component: z^(1/3)

Real Component: z^(1/3)
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2019-03-19 20:19
This example demonstrates the real part of the complex number z^(1/3) as a 3D surface, highlighting geometric properties and symmetry. Key mathematical concepts include complex number operations, power functions, 3D surfaces, vectors, and symmetry. The construction utilizes GeoGebra commands like SelectedIndex, Plane, Surface, button1, variables t, a, b, c, text1, ListBranches, index, d, planeC, points B0, B1, B2 for interactive modeling. Suitable for high school and advanced learners to explore the geometric representation of complex functions and symmetry analysis.

GeoGebra Commands & Parameters

  1. SelectedIndex(ListBranches) → index
  2. Plane(xAxis, yAxis) → planeC
  3. Surface((u * cos(v)), (u * sin(v)), Re((u * cos(v)), (u * sin(v)), 3, 0), u, 0, 2, v, (-π), π - π / 1000) → B0
  4. Surface((u * cos(v)), (u * sin(v)), Re((u * cos(v)), (u * sin(v)), 3, 1), u, 0, 2, v, (-π), π - π / 1000) → B1
  5. Surface((u * cos(v)), (u * sin(v)), Re((u * cos(v)), (u * sin(v)), 3, 2), u, 0, 2, v, (-π), π - π / 1000) → B2