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File:Exponential Function Argument.png

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Description

Diagram of the argument of the exponential function in the complex plane. The plot is given by:

Date
Source Own drawing, Plotted in MuPAD, code given below.
Author Inductiveload
Permission
(Reusing this file)
Public domain 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.
Other versions See Exponential function for related graphics.

MuPAD Code

  q := arg(exp(x+I*y)):

  conts := 10:
  projectionlevel:=-5:
  ylimit := 2*PI:
  xlimit := 3:
  submeshlevel := 0:

colourfunc := zip(RGB::VenetianRed, RGB::DarkBlue,
                  (a, b) -> (q(x,y)+PI)/(6)*a
                           -(q(x,y)-PI)/(6)*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,
                             AdaptiveMesh = 10,
                             FillColorFunction = colourfunc,
                             AxesTitleFont = ["Courier New", Bold, 14],
                             ViewingBoxZRange = -5..PI,
                             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"],
                             ZTicksNumber = None,
                             ZTicksAt = [-PI = "-PI", -PI/2 = "-PI/2",
                                         0 = "0", 
                                         PI/2 = "PI/2", PI = "PI"]
                            ):

contours := plot::modify(funcplot,
                         ZContours = [$ -3.14..3.14 step 0.7853],
                         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 = [$ -3.14..3.14 step 0.7853],
                                                LineWidth = 0.2,
                                                LineColorType = Dichromatic,
                                                LineColor = RGB::VenetianRed.[0.99],
                                                LineColor2 = RGB::DarkBlue.[0.99],
                                                XLinesVisible = FALSE,
                                                YLinesVisible = FALSE,
                                                Filled = FALSE
                                               )
                                  ):
                             
camera := plot::Camera([-40, -120, 60],
                       [-0.5, -1, -0.5],
                       0.1
                      ):
                             
ploteverything := plot::Canvas(funcplot, contours, projcontours,
                               Width = 8.5*unit::inch, 
                               Height = 7*unit::inch,
                               camera
                              ): 
                          
plot(ploteverything)

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25 April 2007

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Date/TimeThumbnailDimensionsUserComment
current19:54, 25 April 2007Thumbnail for version as of 19:54, 25 April 20071,700 × 1,400 (593 KB)Inductiveload{{Information |Description=Diagram of the argument of the exponential function in the complex plane. The plot is given by: ::<math>z=\operatorname{arg} \left (\exp \left( \frac{1}{x + i y} \right)\right)</math> |Source=Own drawing, Plotted in MuPAD, code

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