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Cube Roots of a Complex Number

Cube Roots of a Complex Number
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2014-04-17 00:00
FunctionCoordinate GeometryComplex Number
In collections Roots of Complex Numbers
This worksheet demonstrates the three cube roots of a complex number N. Using GeoGebra, you can observe the distribution pattern of the cube roots. Key mathematical concepts include complex numbers, cube roots, and the geometric representation of complex numbers. Objects such as N, A, p, A_0, A_1, A_2 are used, involving the geometric representation of complex numbers and the calculation of cube roots. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point N(2.0, 0.0)
  2. arg(N)
  3. Numeric p(3.0)
  4. (A + 0) / p
  5. (A + (2 * π)) / p
  6. (A + ((2 * π) * 2)) / p
  7. abs(N)^(1 / p)
  8. (r * ℯ^((ί * A_1)))
  9. (r * ℯ^((ί * A_0)))
  10. (r * ℯ^((ί * A_2)))
  11. Boolean a(true)
  12. A / °
  13. Boolean b(true)
  14. A_0 / °
  15. A_1 / °
  16. A_2 / °
  17. abs(N)
  18. Boolean c(true)
  19. Boolean d(true)
  20. Boolean e(true)

AI Drawing Prompt Reference

Draw the three cube roots of a complex number N. Start by placing point N on the complex plane, then calculate the argument of N. Set parameter p to 3, and use the argument and p to calculate the angles of the three cube roots. Finally, calculate the positions of the three cube roots based on these angles and the modulus of N.
The prompt above was compiled from the original drawing commands and is for reference only.