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.

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

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

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

$\mathrm{ptlist}≔\left[1+2\mathrm{I}\,3+4\mathrm{I}\,5-\mathrm{I}\,7-8\mathrm{I}\right]$

$\mathrm{ptlist}≔\left[1+2\mathrm{I}\,3+4\mathrm{I}\,5-\mathrm{I}\,7-8\mathrm{I}\right]$

$\mathrm{complexplot}\left(\mathrm{ptlist}\,x=0..10\,\mathrm{style}=\mathrm{point}\right)$

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

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

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

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

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

The a, b parameter was updated in Maple 2024.