MathPlotAI Logo MathPlotAI

Complex integration: z^i

Complex integration: z^i
Loading the math board and drawing, please wait…
2021-05-02 17:11
IntegralComplex NumberGeometric Construction
This example demonstrates the geometric and analytical properties of the complex integral z^i. Key mathematical concepts include complex numbers, complex integration, and complex functions. Construction involves GeoGebra commands such as SelectedIndex, Midpoint, Distance, Element, Segment, Derivative, etc. Suitable for high school students or undergraduate students learning complex analysis fundamentals.

GeoGebra Commands & Parameters

  1. SelectedIndex(pathNames) → pathIndex
  2. Midpoint(A, B) → M
  3. Distance(A, B) → distAB
  4. Element(pathList, pathIndex) → path
  5. Segment(path(0.3), path(0.3 + 0.01)) → arrow1
  6. Segment(path(0.6), path(0.6 + 0.01)) → arrow2
  7. Element(X, pathIndex) → Rezt
  8. Element(Y, pathIndex) → Imzt
  9. Derivative(Rezt, t) → dRezt
  10. Derivative(Imzt, t) → dImzt
  11. SelectedIndex(plotNames) → plotIndex
  12. Ray((0, 0), (-1, 0)) → brachCut
  13. SelectedIndex(branchNames) → branchIndex

AI Drawing Prompt Reference

Draw the integral graph of z^i, including the geometric and analytical properties of complex numbers, complex integration, and complex functions. First, draw a complex path on the complex plane, then calculate the real and imaginary parts at each point on the path, next find the derivatives of the real and imaginary parts, and finally draw the branch cut line.
The prompt above was compiled from the original drawing commands and is for reference only.