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 may be given as an algebraic expression or a procedure.  Alternatively, a list of points may be provided.  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 real parameter t over the parameter range $a..b$.

The second calling sequence, complexplot(f, a..b), plots the complex function represented by f, a procedure taking a single real parameter and returning a complex value, over the parameter 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 may 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.

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

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

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

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

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

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

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

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