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 complexplot
 create a 2-D complex plot

 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

 > $\mathrm{with}\left(\mathrm{plots}\right):$

Plot an expression over a parameter range.

 > $\mathrm{complexplot}\left(\mathrm{sin}\left(x+I\right),x=-\mathrm{\pi }..\mathrm{\pi }\right)$

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

 > $\mathrm{complexplot}\left(\mathrm{cos}+\mathrm{sin}I,-\mathrm{\pi }..\mathrm{\pi },-0.8..0.8,-1..1\right)$

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

 > $\mathrm{ptlist}≔\left[1+2I,3+4I,5-I,7-8I\right]$
 ${\mathrm{ptlist}}{≔}\left[{1}{+}{2}{}{I}{,}{3}{+}{4}{}{I}{,}{5}{-}{I}{,}{7}{-}{8}{}{I}\right]$ (1)
 > $\mathrm{complexplot}\left(\mathrm{ptlist},x=0..10,\mathrm{style}=\mathrm{point}\right)$

Complex ranges give phase plots:

 > $\mathrm{complexplot}\left(\mathrm{arctanh},-2-I..2+I\right)$

The color bar can be removed:

 > $\mathrm{complexplot}\left(\mathrm{arcsinh}\left(z\right),z=-2-I..2+I,\mathrm{colorbar}=\mathrm{false}\right)$

Or customized:

 > $\mathrm{complexplot}\left(\mathrm{arcsinh}\left(z\right),z=-2-I..2+I,\mathrm{colorbar}=\left['\mathrm{barcaption}'=\mathrm{typeset}\left(\mathrm{arg}\left(f\left(z\right)\right)\right)\right],\mathrm{colorscheme}="ColorWheel"\right)$

The command to create the plot from the Plotting Guide is

 > $\mathrm{complexplot}\left(\mathrm{cos}+\mathrm{sin}I,-\mathrm{\pi }..\mathrm{\pi },\mathrm{labels}=\left["Re","Im"\right]\right)$

Compatibility

 • The plots[complexplot] command was updated in Maple 2024.
 • The a, b parameter was updated in Maple 2024.

 See Also