虚数轨道
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所属专题
Complex Math
①这个范例演示了虚数在复平面上的运动轨迹;②涉及的核心数学概念包括复数、向量、变换和轨迹;③作图要点使用了GeoGebra命令Polygon(多边形)、Segment(线段)、Vector(向量)、Translate(平移)、Intersect(交点);④适合高中数学学习,用于理解复数的几何意义和动态变化。
GeoGebra 命令及参数
Polygon(z_1, z_2, z_τ) → poly1, z_3, z_4, z_5Segment(z_6, z_2) → aSegment(z_6, z_τ) → bSegment(z_6, z_1) → cSegment(z_2, z_7) → dSegment(z_7, z_6) → eSegment(z_1, z_7) → iPolygon(z_1, z_6, z_τ) → poly2, z_8, z_9, z_{10}Polygon(z_τ, z_2, z_6) → poly3, z_{11}, z_{12}, z_{13}Polygon(z_6, z_7, z_2) → poly4, z_{14}, z_{15}, z_{16}Polygon(z_7, z_1, z_6) → poly5, z_{17}, z_{18}, z_{19}Vector(A, B) → uTranslate(z_1, u) → z_{9}Translate(z_2, u) → z_{20}Translate(z_τ, u) → z_{21}Polygon(z_{9}, z_{20}, z_{21}) → poly1', z_{22}, z_{23}, z_{24}Vector(C, D) → vTranslate(z_1, v) → z_{25}Translate(z_6, v) → z_{26}Translate(z_τ, v) → z_{27}Polygon(z_{25}, z_{26}, z_{27}) → poly2', z_{28}, z_{29}, z_{30}Vector(E, F) → wTranslate(z_6, w) → z_{31}Translate(z_7, w) → z_{32}Translate(z_2, w) → z_{33}Polygon(z_{31}, z_{32}, z_{33}) → poly4', z_{34}, z_{35}, z_{36}Vector(G, H) → jTranslate(z_7, j) → z_{37}Translate(z_1, j) → z_{38}Translate(z_6, j) → z_{39}Polygon(z_{37}, z_{38}, z_{39}) → poly5', z_{40}, z_{41}, z_{42}Intersect(z_{28}, z_{29}) → IIntersect(z_{41}, z_{42}) → JSegment(I, J) → lIntersect(z_{28}, z_{30}) → KIntersect(z_{40}, z_{41}) → LSegment(K, L) → mIntersect(z_{29}, z_{30}) → MIntersect(z_{40}, z_{42}) → NSegment(M, N) → nIntersect(z_{22}, z_{24}) → OIntersect(z_{34}, z_{36}) → PSegment(O, P) → qIntersect(z_{23}, z_{24}) → QSegment(Q, P) → rIntersect(xAxis, yAxis) → RIntersect(g, p, (-8.254196448459108, 3.275891323225046E-6)) → SIntersect(g, p, (-8.254196448459108, 3.275891323225046E-6)) → TSegment(R, z_τ) → sSegment(z_{46}, z_{44}) → a_1Segment(z_{45}, z_{43}) → b_1