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Drawing Loci of the Form arg(z-a)=θ

Drawing Loci of the Form arg(z-a)=θ
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2020-08-02 20:14
Complex NumberGeometric ConstructionLocus
This example demonstrates how to draw loci in the complex plane defined by arg(z-a)=θ, which are rays emanating from point a at angle θ. Key math concepts include complex numbers, argument, and geometric construction. GeoGebra commands like If, Segment, Rotate, Angle, and Ray are used to construct the rays. Suitable for high school mathematics education to understand the relationship between complex number arguments and loci.

GeoGebra Commands & Parameters

  1. If(b < 0, "-", "+") → text11
  2. Segment(A, C) → f
  3. Rotate(C, θ, A) → C'
  4. Angle(C, A, C') → α
  5. Ray(A, C') → g
  6. If(a < 0, "+", "-") → text12
  7. If(b < 0, "+", "-") → text13

AI Drawing Prompt Reference

In the complex plane, start from a fixed point and draw a ray emanating from it, making a specified angle with the positive real axis. At the starting point, construct an angle marker showing that angle value. Near the point, add text labels indicating the signs of the real and imaginary parts (positive or negative) to clarify the quadrant. The figure illustrates the locus of points whose argument equals the given angle, which is a ray from the point in a fixed direction.
The prompt above was compiled from the original drawing commands and is for reference only.