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Complex Transformations of a Circle

Complex Transformations of a Circle
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2014-02-23 00:13
CircleComplex NumberTransformation
This example demonstrates various mappings of a circle under complex transformations by dragging the red points. It covers the concept of complex numbers, the geometric properties of circles, and the patterns of complex transformations. It uses commands like Circle, Point, Locus in GeoGebra, suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → Z
  3. Locus(u, Z) → loc2
  4. Locus(v, Z) → loc3
  5. Locus(w, Z) → loc1

AI Drawing Prompt Reference

Draw a circle and place a movable point Z on it. Then, create three loci: the first one is the rotation of Z around the circle's center, the second one is the movement of Z along the circumference, and the third one is the movement of Z along the diameter.
The prompt above was compiled from the original drawing commands and is for reference only.