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Powers of a Complex Number

Powers of a Complex Number
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2016-10-24 19:15
FunctionCoordinate GeometryComplex Number
In collections UNSW MATH1131/1231 Algebra material
This example demonstrates the geometric representation of powers of a complex number in the complex plane. Key math concepts include complex numbers, polar form, exponential function, modulus, and argument. Construction highlights involve using CurveCartesian for plotting, LaTeX for text display, and objects like c, b, B, list1, text1 for visualizing operations. Suitable for high school and above, helping students understand the geometric meaning and visualization of complex number operations.

GeoGebra Commands & Parameters

  1. CurveCartesian(((x(A)^(2) + y(A)^(2))^(t / 2) * cos((t * atan2(y(A),x(A))))), ((x(A)^(2) + y(A)^(2))^(t / 2) * sin((t * atan2(y(A),x(A))))), t, 1, 6) → d
  2. LaTeX((((("z=(" * x(A)) * ") + (") * y(A)) * ")i")) → text3