MathPlotAI Logo MathPlotAI

Complex Number Addition by Susan Addington

Complex Number Addition by Susan Addington
Loading the math board and drawing, please wait…
2016-04-09 02:32
VectorComplex NumberTransformation
This example demonstrates complex number addition as a geometric transformation: translation. Using points, vectors, and the translate command, it shows how complex number addition is performed geometrically. Key mathematical concepts include complex numbers, translation, and vectors. Suitable for students in middle school and above to learn the geometric meaning of complex number addition.

GeoGebra Commands & Parameters

  1. Line(Q, R) → j
  2. Point(j) → S
  3. Circle(D, E) → d
  4. Point(d) → J
  5. Polygon(A_2, B, C) → poly1, c, a_1, b
  6. Vector(F, G) → u
  7. OrthogonalLine(F, u) → e_1
  8. Point(e_1) → H
  9. Translate(G, u) → G'_1
  10. Translate(H, u) → H'_1
  11. Polygon(F, H, H'_1, G) → poly2, f, h, h', g
  12. Vector(F, G'_1) → v
  13. Translate(F, v) → F'
  14. Translate(H, v) → H'
  15. Translate(H'_1, v) → I
  16. Translate(G, v) → G'
  17. Polygon(F', H', I, G') → poly2', f', h'_1, i, g'
  18. Translate(F', v) → F''
  19. Translate(H', v) → H''
  20. Translate(I, v) → I'
  21. Translate(G', v) → G''
  22. Polygon(F'', H'', I', G'') → poly2'', f'', h'', i', g''
  23. Point(poly1) → L
  24. Point(poly2) → M
  25. Point(poly2') → N
  26. Point(poly2'') → O_1
  27. Locus(z, J) → loc1
  28. Locus(z_1, L) → loc2
  29. Locus(z_2, M) → loc3
  30. Locus(z_3, N) → loc4
  31. Locus(z_4, O_1) → loc5
  32. Intersect(xAxis, yAxis) → O
  33. Circle(O, 1) → k
  34. Locus(z_5, S) → loc6
  35. Vector(O, a) → w
  36. Translate(K, w) → K'
  37. Vector(K, K') → p
  38. Polygon(T, U, 5) → poly3, t, u_1, q, r, s, V, W, Z
  39. Polygon(T, W, U, Z, V) → poly4, t_1, w_1, u_2, z_6, v_1
  40. Point(poly4) → A_1
  41. Locus(z_7, A_1) → loc7

AI Drawing Prompt Reference

Create a coordinate-plane diagram illustrating complex-number addition as translation. Draw a line and a circle with points on them, then construct a triangle and a rectangle determined by a vector and a perpendicular through its start. Translate this rectangle repeatedly along the vector to form a chain of congruent rectangles. Place points on the triangle and each rectangle and generate their loci as parameters vary. Also draw the unit circle centered at the origin, a vector from the origin, a translated point and the resulting vector, and construct a regular pentagon together with its star-shaped vertex connection, ending with a point on the star and its locus.
The prompt above was compiled from the original drawing commands and is for reference only.