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Squaring Complex Numbers

Squaring Complex Numbers
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2020-05-05 00:23
Coordinate GeometryComplex NumberGeometric Construction
This example demonstrates how to represent the square of a complex number using geometric construction. Key mathematical concepts include complex numbers, vectors, and geometric construction. It uses commands like Polygon, Angle, and If in GeoGebra. Suitable for middle school and above students to learn the geometric representation and operations of complex numbers.

GeoGebra Commands & Parameters

  1. Polygon(z_2, z_3, z_1) → t1, f, g, h
  2. Angle(z_3, z_2, z_1) → α
  3. If(a ≤ 1, ℯ^(((a * α) * ί)), (ℯ^((α * ί)) * (((abs(z_1) - 1) * (a - 1)) + 1))) → z_4
  4. Polygon(z_2, z_6, z_5) → t2, i, j, k