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Phase Shifts of Complex Numbers

Phase Shifts of Complex Numbers
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2020-02-03 09:55
TrigonometryComplex NumberGeometric ConstructionGraphing
This example demonstrates the phase shifts of complex numbers in the complex plane. It involves core math concepts like complex numbers, phase, rotation, and geometric representation. The construction uses GeoGebra commands/objects: b, c, f, g, text3, A, B, pic1, text1, text2 for constructing complex number representations, movement trajectories, and annotations. Suitable for high school and above students to understand the geometric meaning of complex operations and phase transformations.

GeoGebra Commands & Parameters

  1. Numeric b(1)
  2. Numeric c(2)
  3. f(x) = imaginary((ℯ^(((ί * b) * x)) * ℯ^((c * ί))))
  4. g(x) = imaginary(ℯ^(((b * x) * ί)))
  5. Point A(12.7, 1.7)
  6. Point B(15.7, 1.7)