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The Complex Exponential Function z->e^z Generally Has Multiple Values

The Complex Exponential Function z->e^z Generally Has Multiple Values
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2017-07-29 02:49
FunctionTrigonometryComplex Number
This example demonstrates that the complex exponential function z->e^z generally has multiple values. The key mathematical concepts involved are complex numbers and exponential functions. The construction uses the CurveCartesian and Textfield commands. It is suitable for high school mathematics education, particularly in the topics of complex numbers and functions.

GeoGebra Commands & Parameters

  1. CurveCartesian((ℯ^((r * cos(t))) * cos((r * sin(t)))), (ℯ^((r * cos(t))) * sin((r * sin(t)))), t, (-π), π) → EXP
  2. Textfield(s) → InputBox1

AI Drawing Prompt Reference

Plot the complex exponential function e^z, where z is a complex number. Use parameter t ranging from -π to π to draw the curve, showing the multi-valued nature of e^z in the complex plane. Add a text input box to enter or display relevant information.
The prompt above was compiled from the original drawing commands and is for reference only.