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Imaginary Component of Logarithm of a Complex Number

Imaginary Component of Logarithm of a Complex Number
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2019-03-19 20:31
FunctionCoordinate GeometryComplex Number
This example demonstrates the imaginary component of the logarithm of a complex number. Key mathematical concepts include complex numbers and logarithmic functions. Using GeoGebra commands such as Surface, button1, t, a, b, c, Im, text1, RSIm, text2, B0, B1, B2, B3, B4, the imaginary part of the complex logarithm can be visualized. Suitable for high school mathematics education and learning about complex logarithms.

GeoGebra Commands & Parameters

  1. Surface((u * cos(v)), (u * sin(v)), Im((u * cos(v)), (u * sin(v))), u, 0, 3, v, (-π), π - π / 200) → RSIm
  2. Surface((u * cos(v)), (u * sin(v)), (0 * (1 - t)) + (Im((u * cos(v)), (u * sin(v))) * If[0 ≤ t ≤ 1, t, 1]) + (0 * (2 - t)) + (((2 * π) * (0 - 2)) * (t - 1)), u, 0, 2, v, (-π), π - π / 1000) → B0
  3. Surface((u * cos(v)), (u * sin(v)), (0 * (1 - t)) + (Im((u * cos(v)), (u * sin(v))) * If[0 ≤ t ≤ 1, t, 1]) + (0 * (2 - t)) + (((2 * π) * (1 - 2)) * (t - 1)), u, 0, 2, v, (-π), π - π / 1000) → B1
  4. Surface((u * cos(v)), (u * sin(v)), (0 * (1 - t)) + (Im((u * cos(v)), (u * sin(v))) * If[0 ≤ t ≤ 1, t, 1]) + (0 * (2 - t)) + (0 * (t - 1)), u, 0, 2, v, (-π), π - π / 1000) → B2
  5. Surface((u * cos(v)), (u * sin(v)), (0 * (1 - t)) + (Im((u * cos(v)), (u * sin(v))) * If[0 ≤ t ≤ 1, t, 1]) + (0 * (2 - t)) + (((2 * π) * (3 - 2)) * (t - 1)), u, 0, 2, v, (-π), π - π / 1000) → B3
  6. Surface((u * cos(v)), (u * sin(v)), (0 * (1 - t)) + (Im((u * cos(v)), (u * sin(v))) * If[0 ≤ t ≤ 1, t, 1]) + (0 * (2 - t)) + (((2 * π) * (4 - 2)) * (t - 1)), u, 0, 2, v, (-π), π - π / 1000) → B4