complexplot - Maple Help
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plots

  

complexplot

  

create a 2-D complex plot

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

complexplot(expr, t=a..b, xv, yv, options)

complexplot(f, a..b, xv, yv, options)

complexplot(L, xv, yv, options)

Parameters

expr

-

algebraic; expression in parameter t defining a curve

t

-

name; curve parameter

f

-

procedure; procedure in one variable defining a curve

a, b

-

realcons; endpoints of parameter range, or complexcons; corners of a complex parameter square

L

-

list; complex numbers specified as points

xv

-

(optional) range or name=range; view of horizontal axis

yv

-

(optional) range or name=range; view of vertical axis

options

-

(optional) sequence of equations; plot options

Description

• 

The complexplot command creates a 2-D plot displaying complex values, with the x-direction representing the real part and the y-direction representing the imaginary part.  The complex function can be given as an algebraic expression or a procedure.  Alternatively, a list of points can be provided.  If a and b are real values, a parametric curve of the complex values of the function is plotted, and if a and b are complex values, then a phase plot is displayed, which is a densityplot with the color of each point corresponding to the argument of the complex function at the point.  For 3-D complex plots, see plots:-complexplot3d.

• 

The first calling sequence, complexplot(expr, t=a..b), plots the complex expression expr which is a function of a single parameter t over the real or complex range a..b.

• 

The second calling sequence, complexplot(f, a..b), plots the complex function represented by f, a procedure taking a single parameter and returning a complex value, over the range a..b.  For more information about plotting procedures using operator notation, see plot/function.

• 

The third calling sequence, complexplot(L), plots a list of complex values as points.  The points are connected unless the style=point option is given.

• 

For all three calling sequences, additional arguments having the form u=v..w or v..w can be provided, where u is a name and v and w are real constants.  If one such argument is provided, it defines the view of the x-axis.  If two are provided, they define the views of the x-axis and y-axis. The name u is used as the axis label if given.

• 

Phase plots automatically include a color bar for the phase coloring. It can be removed with the option colorbar=false, and it can be customized by passing in a list of options as described in the plot/colorbar help page.

• 

Remaining arguments are interpreted as options as described in the plot/options help page.

Examples

withplots:

Plot an expression over a parameter range.

complexplotsinx+I,x=π..π

Plot a procedure over a parameter range, with a restricted view.

complexplotcos+sinI,π..π,0.8..0.8,1..1

Plot a list of points and display using an x-axis view of 0..10.

ptlist1+2I,3+4I,5I,78I

ptlist1+2I,3+4I,5I,78I

(1)

complexplotptlist,x=0..10,style=point

Complex ranges give phase plots:

complexplotarctanh,2I..2+I

The color bar can be removed:

complexplotarcsinhz,z=2I..2+I,colorbar=false

Or customized:

complexplotarcsinhz,z=2I..2+I,colorbar=barcaption=typesetargfz,colorscheme=ColorWheel

The command to create the plot from the Plotting Guide is

complexplotcos+sinI,π..π,labels=Re,Im

Compatibility

• 

The plots[complexplot] command was updated in Maple 2024.

• 

The a, b parameter was updated in Maple 2024.

See Also

plot

plot/function

plot/options

plots

plots:-complexplot3d