DescriptionExponential Function Argument.png	Diagram of the argument of the exponential function in the complex plane. The plot is given by: ${\displaystyle z=\operatorname {arg} \left(\exp \left(x+iy\right)\right)}$
Date	25 April 2007
Source	Own drawing, Plotted in MuPAD, code given below.
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.
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)