MathPlotAI Logo MathPlotAI

Complex Numbers Squaring Map

Complex Numbers Squaring Map
Loading the math board and drawing, please wait…
2018-09-17 01:09
FunctionCoordinate GeometryComplex Number
This example demonstrates the mapping of complex number squaring in the complex plane. It involves core mathematical concepts like complex numbers, function mapping, and coordinate geometry. Construction highlights include the use of GeoGebra commands and objects such as SelectedElement, Sequence, Join, Circle, CurveCartesian, and Segment. Suitable for high school and above learners to understand the geometric meaning of complex operations and function graphing.

GeoGebra Commands & Parameters

  1. SelectedElement(L_2) → points
  2. Sequence((cos(w), sin(w)), w, 0, (2 * π) - π / points, (2 * π / points)) → L_1
  3. Join({L_1, L_1}) → L_3
  4. Circle((0, 0), 1 / 3) → c
  5. Circle(((2 / 3 * cos(t)), (2 / 3 * sin(t))), 1 / 3) → d
  6. CurveCartesian((2 / 3 * cos(w)) + (1 / 3 * cos((2 * w))), (2 / 3 * sin(w)) + (1 / 3 * sin((2 * w))), w, 0, t) → a
  7. Segment(((2 / 3 * cos(t)), (2 / 3 * sin(t))), A) → f
  8. Circle((0, 0), 1) → e
  9. Sequence(Segment[L_3(w + 1), L_3((2 * w) + 1)], w, 1, (90 * t / π)) → L_4