Multiplication by Powers of i

Multiplication by Powers of i
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2018-08-11 06:02
This example demonstrates the geometric meaning of multiplying complex numbers by powers of i, showing the rotation of complex numbers in the complex plane. Key math concepts include complex numbers, rotation, and geometric representation. Construction highlights the use of commands and objects like Point, Polygon, Textfield, Angle, Rotate, with elements such as points A, B, C, D, E, polygon poly1, and variables a, b, c, d, e, z_A, z_B, n. Suitable for high school mathematics education to understand the geometric intuition of complex number operations.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 4]) → B
  2. Polygon(A, B, C, D, E) → poly1, a, b, c, d, e
  3. Textfield(n) → InputBox1
  4. Angle(Translate[B, Vector[A, A']], A', B') → ang
  5. Rotate(Polygon[Translate[A, Vector[A, A']], Translate[B, Vector[A, A']], Translate[C, Vector[A, A']], Translate[D, Vector[A, A']], Translate[E, Vector[A, A']]], ang, A') → poly2