Complex Multiplication as Geometric Transformation

GeoGebra Commands & Parameters

1. Intersect(xAxis, yAxis) → P
2. Circle(P, 1) → k
3. Intersect(k, xAxis) → D_1, E_1
4. Line(Q, R) → j
5. Point(j) → S
6. Circle(D, E) → d
7. Point(d) → J_1
8. Polygon(A, B, C) → poly1, c, a_1, b
9. Vector(F, G) → u
10. OrthogonalLine(F, u) → e_1
11. Point(e_1) → H
12. Translate(G, u) → G'_1
13. Translate(H, u) → H'_1
14. Polygon(F, H, H'_1, G) → poly2, f, h, h', g
15. Vector(F, G'_1) → v
16. Translate(F, v) → F'
17. Translate(H, v) → H'
18. Translate(H'_1, v) → I
19. Translate(G, v) → G'
20. Polygon(F', H', I, G') → poly2', f', h'_1, i, g'
21. Translate(F', v) → F''
22. Translate(H', v) → H''
23. Translate(I, v) → I'
24. Translate(G', v) → G''
25. Polygon(F'', H'', I', G'') → poly2'', f'', h'', i', g''
26. Point(poly1) → L
27. Point(poly2) → M
28. Point(poly2') → N
29. Point(poly2'') → O
30. Locus(z, J_1) → loc1
31. Locus(z_1, L) → loc2
32. Locus(z_2, M) → loc3
33. Locus(z_3, N) → loc4
34. Locus(z_4, O) → loc5
35. Locus(z_5, S) → loc6
36. Vector(P, a) → w
37. Point(k) → K
38. Line(z_6, z_5) → q
39. Intersect(q, j) → T
40. Polygon(U, V, 5) → poly3, u_1, v_1, r, s, t, W, Z, A_1
41. Polygon(U, Z, V, A_1, W) → poly4, u_2, z_7, v_2, a_2, w_1
42. Point(poly4) → B_1
43. Locus(z_8, B_1) → loc7
44. Intersect(yAxis, xAxis) → C_1
45. Angle(D_1, P, a) → α
46. Segment(C_1, J) → d_1
47. Segment(C_1, J') → f_1
48. Angle(J, C_1, J') → ε
49. Segment(C_1, a) → g_1