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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 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 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.

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

The command to create the plot from the Plotting Guide is

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