Complex Exponential and Logarithm Functions

Manipulate[plottype[part@func[x+I y],{x,-lowx,lowx},{y,-lowy,
lowy},AxesLabel->Automatic,
PlotLabel->Style[Framed[TraditionalForm[part@func[z]]],16,Blue,Background->Lighter[Yellow]],ColorFunction->"Rainbow",ImageSize->{400,300},ImagePadding->If[plottype==Plot3D,30,{{20,20},{20,50}}]],{{plottype,Plot3D,""},{Plot3D->"3D plot",ContourPlot->"contour plot"}},{{part,Re,""},{Re->"real part",Im->"imaginary part",Abs->"absolute value"}},{{func,Exp,"function"},
Evaluate@Flatten[{#->TraditionalForm[#[z]]}&/@{Exp,Log,Cos,Sin,Cosh, Sinh}]},
{{lowx,5,"x interval"},0.1,15},
{{lowy,8,"y interval"},0.1,15}]

CAPTION

The complex exponential and logarithm functions can be visualized by looking at the real and imaginary part of the function and its absolute value. Other combinations of the exponential functions such as the trigonometric sine and cosine, or the hyperbolic sine and cosine can also be visualized.

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Complex Exponential and Logarithm Functions" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ComplexExponentialAndLogarithmFunctions/

Contributed by: Alain Goriely

Based on a program by: Rob Morris

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