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Multiplication and Division of Complex Numbers in Modulus-Argument Form (1)

Multiplication and Division of Complex Numbers in Modulus-Argument Form (1)
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2018-04-23 01:51
FunctionComplex NumberGeometric Construction
This example demonstrates the multiplication and division of complex numbers in modulus-argument form. Key mathematical concepts include the modulus and argument of complex numbers. Using commands and objects like Intersect, Segment, Angle, etc., the process of multiplication and division is clearly illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Segment(O, z_1) → f
  3. Angle((3, 0), O, z_1, xAxis) → α
  4. Segment(O, z_2) → g
  5. Angle((3, 0), O, z_2, xAxis) → β
  6. Segment(O, z_3) → h
  7. Angle((3, 0), O, z_3) → ζ
  8. Segment(O, z_4) → i
  9. Angle((3, 0), O, z_4) → θ
  10. If(δ < 0, "-", "+") → mult
  11. If(θ_2 < 0, "+", "-") → div

AI Drawing Prompt Reference

Draw a coordinate system with the origin and x, y axes. Plot four vectors representing complex numbers, labeling their angles with the x-axis. Illustrate the multiplication and division of two complex numbers using auxiliary lines and angles to clearly show the geometric meaning of these operations.
The prompt above was compiled from the original drawing commands and is for reference only.