Adding Complex Numbers and the Parallelogram Rule

Adding Complex Numbers and the Parallelogram Rule
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2012-11-12 09:11
In collections complex numbers
① This example demonstrates the addition of two complex numbers on the complex plane and shows the parallelogram formed by the two addends and the origin. ② Core mathematical concepts include the geometric representation of complex numbers, vector addition, the parallelogram law, and translation transformations. ③ Construction highlights: GeoGebra commands Intersect, Segment, Distance, and Polygon are used to create objects z_1, z_2, z_3, a, b, c, d, poly1, representing the two addends, their sum, the vector segments, and the parallelogram region. ④ Suitable for high‑school mathematics (complex numbers elective) or introductory university courses, ideal for classroom demonstration, self‑study exploration, or inclusion in a teaching resource library.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → B
  2. Segment(B, z_1) → a
  3. Segment(B, z_2) → b
  4. Segment(B, z) → c
  5. Distance(a, c) → d
  6. Polygon(B, z_1, z, z_2) → poly1, b_1, a_1, z_3, c_1