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Real Component: (1-z^2)^(1/2)

Real Component: (1-z^2)^(1/2)
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2019-03-19 20:13
FunctionCoordinate GeometryComplex Number
This example demonstrates the real part of the expression (1-z^2)^(1/2). Key mathematical concepts include complex numbers and coordinate geometry. Using commands like Surface and Rectangle in GeoGebra, the real part of the expression can be graphed. Suitable for high school mathematics education or students learning complex numbers and coordinate geometry.

GeoGebra Commands & Parameters

  1. SelectedIndex(ListBranches) → index
  2. Surface((u * cos(v)), (u * sin(v)), Re((u * cos(v)), (u * sin(v)), 2, 0), u, 0, 2, v, (-π), π) → B0
  3. Surface((u * cos(v)), (u * sin(v)), Re((u * cos(v)), (u * sin(v)), 2, 1), u, 0, 2, v, (-π), π) → B1

AI Drawing Prompt Reference

Plot the real part of the expression (1-z^2)^(1/2). First, draw a unit circle on the complex plane. Then, use the Surface command to plot the real part when u varies from 0 to 2 and v varies from -π to π.
The prompt above was compiled from the original drawing commands and is for reference only.