MathPlotAI Logo MathPlotAI

Limits of Complex Functions

Limits of Complex Functions
Loading the math board and drawing, please wait…
2015-02-20 13:28
FunctionLimitComplex Number
In collections Mapping Diagrams to Visualize Complex Analysis
This example illustrates the concept of limits for complex functions. By adjusting parameters, observe the behavior of the function in the complex plane. Key mathematical concepts include complex numbers, limits, and functions. GeoGebra commands used include Sequence, CurveCartesian, Textfield, Vector, PointIn, Circle, etc. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence((δ * (cos(t) + (sin(t) * ί))) + x(z_0) + (y(z_0) * ί), t, -3.14159, 3.141592653589793, 0.5236) → z_*
  2. Sequence((x(Element[fz_*, k]), y(Element[fz_*, k]), height_{image}), k, 1, 12) → fpoint_*
  3. Sequence(Vector[Element[z_*, j], Element[fpoint_*, j]], j, 1, 12) → fvec_*
  4. CurveCartesian((δ * cos(t)), (δ * sin(t)), height_{image}, t, 0, 6.283185307179586) → d
  5. Textfield(fz_*) → inputBox1
  6. Vector(z_#, f_{(z#).}) → w
  7. Textfield(f_{(z#)}) → inputBox2
  8. CurveCartesian(t, 0, height_{image}, t, -5, 5) → Xh
  9. CurveCartesian(0, t, height_{image}, t, -5, 5) → Yh
  10. Textfield(z_*) → inputBox3
  11. PointIn(C_{image}) → L
  12. Circle(L, ε, Vector[(0, 0, 1)]) → f