File:Exponential Function (Abs Imag Part).png

DescriptionExponential Function (Abs Imag Part).png	Diagram of the absolute value of the imaginary part of exponential function in the complex plane. The surface is given by: ${\displaystyle z={\bigg |}\operatorname {Im} \left(\exp \left(x+iy\right)\right){\bigg |}}$
Date	20 April 2007
Source	Own drawing, Plotted in MuPAD
Author	Inductiveload
Permission (Reusing this file)	Public domainPublic domainfalsefalse I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

MuPAD Code[edit]

  q := abs(Im(exp(x+I*y))):

  conts := 21:
  projectionlevel:=-10:
  ylimit := 2*PI:
  xlimit := 3:
  submeshlevel := 5:

zmin := -10:
zmax := 10:
color := zip(RGB::SapGreen, RGB::LightBlue,
             (a, b) -> (q(x,y)-zmin)/(zmax-zmin)*a
                      +(zmax-q(x,y))/(zmax-zmin)*b):

funcplot := plot::Function3d(q(x,y),
                             x = -xlimit..xlimit,
                             y = -ylimit..ylimit,
                             Mesh = [23, 23],
                             Submesh = [submeshlevel,submeshlevel],
                             LineColor = RGB::Black.[0.4],
                             LineWidth = 0.15,
                             FillColorFunction = color,
                             AxesTitleFont = ["Courier New", Bold, 14],
                             ViewingBoxZRange = -10..10,
                             YTicksNumber = None,
                             YTicksAt = [-3*PI/2 = "-3 PI/2", -PI = "-PI", -PI/2 = "-PI/2", -2*PI = "-2 PI",
                                         0 = "0", 
                                         PI/2 = "PI/2", PI = "PI",  3*PI/2 = "3 PI/2", 2*PI = "2 PI"]
                            ):

contours := plot::modify(funcplot,
                         ZContours = [Automatic, conts],
                         LineWidth = 0.2,
                         LineColor = RGB::Gray90.[0.5],
                         XLinesVisible = FALSE,
                         YLinesVisible = FALSE,
                         Filled = FALSE
                        ):
                        
projcontours := plot::Transform3d([0, 0, projectionlevel],
                                  [1, 0, 0, 0, 1, 0, 0, 0, 0], 
                                   plot::modify(funcplot, ZContours = [Automatic, conts],
                                                LineWidth = 0.2,
                                                LineColorType = Dichromatic,
                                                LineColor = RGB::DarkGreen.[0.99],
                                                LineColor2 = RGB::Yellow.[0.99],
                                                XLinesVisible = FALSE,
                                                YLinesVisible = FALSE,
                                                Filled = FALSE
                                               )
                                  ):
                             
camera := plot::Camera([25, 80, 120],
                       [0.5, 1, 0],
                       0.15
                      ):
                             
ploteverything := plot::Canvas(funcplot, contours, projcontours,
                               Width = 8.5*unit::inch, 
                               Height = 7*unit::inch,
                               camera
                              ): 
                          
plot(ploteverything)