create a 3-D complex plot - Maple Help

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plots[complexplot3d] - create a 3-D complex plot

 Calling Sequence complexplot3d([expr1, expr2], x=a..b, y=c..d) complexplot3d([f1, f2],  a.. b,  c.. d) complexplot3d(expr3, z=a + b*I..c + d*I) complexplot3d(f2, a + b*I..c + d*I)

Parameters

 expr1, expr2 - algebraic; expressions in parameters x and y f1, f2 - procedures; functions to be plotted expr3 - algebraic; expression in parameter z a, b, c, d - realcons; endpoints of parameter ranges

Description

 • The four different calling sequences to the complexplot3d function above all define plots in three space for expressions or procedures mapping

${R}^{2}\to {R}^{2}\mathrm{or}C\to C.$

 For 2-D complex plots, see plots/complexplot.
 • For plotting functions from ${R}^{2}$ to ${R}^{2}$ complexplot3d plots the first component while coloring the graphic using the second component.
 • For plotting functions from C to C complexplot3d plots the magnitude of the function while coloring the resulting surface using the argument of the function.
 • The first two calls plot expressions and procedures, respectively, from ${R}^{2}$ to ${R}^{2}$. In the second case f1 and f2 take two arguments and return a real value. The form of the range specifications determine whether an expression or a procedure is to be plotted. The last two calls plot expressions and procedures, respectively, from C to C.
 • The range components a, b, c, and d must evaluate to real constants. Note that operator notation is used in the second and fourth calls, that is, the procedure name is given without parameters specified, and the ranges must be given simply in the form a..b, rather than as an equation.
 • Any additional arguments are interpreted as options as described in the plot3d/options help page.  For example, the option $\mathrm{grid}=\left[m,n\right]$ where m and n are positive integers specifies that the plot is to be constructed on an m by n grid instead of on the default 25 by 25 grid.

Examples

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

Plot a complex procedure:

 > $f:=z→\mathrm{sec}\left(z\right)$
 ${f}{:=}{z}{→}{\mathrm{sec}}{}\left({z}\right)$ (1)
 > $\mathrm{complexplot3d}\left(f,-2-2I..2+2I\right)$

Plot an expression from ${R}^{2}$ to ${R}^{2}$, where the plot is of the first component colored by the second component:

 > $\mathrm{complexplot3d}\left(\left[{x}^{2}-{y}^{2},2xy\right],x=-2..2,y=-2..2\right)$

Repeat the previous example using operator form.

 > $\mathrm{f1}:=\left(x,y\right)→{x}^{2}-{y}^{2};$$\mathrm{f2}:=\left(x,y\right)→2xy$
 ${\mathrm{f1}}{:=}\left({x}{,}{y}\right){→}{{x}}^{{2}}{-}{{y}}^{{2}}$
 ${\mathrm{f2}}{:=}\left({x}{,}{y}\right){→}{2}{}{x}{}{y}$ (2)
 > $\mathrm{complexplot3d}\left(\left[\mathrm{f1},\mathrm{f2}\right],-2..2,-2..2\right)$

Plot an image created from Newton's iteration:

 > $f:=z→z-\frac{{z}^{3}-2}{3{z}^{2}}$
 ${f}{:=}{z}{→}{z}{-}\frac{{1}}{{3}}{}\frac{{{z}}^{{3}}{-}{2}}{{{z}}^{{2}}}$ (3)
 > $\mathrm{complexplot3d}\left({f}^{\left(4\right)},-3-3I..3+3I,\mathrm{view}=-4..4,\mathrm{grid}=\left[50,50\right]\right)$

Plot $\left|f\left(z\right)\right|$, where $z=r{ⅇ}^{I\mathrm{\theta }}$ and $f\left(z\right)=\frac{z}{{ⅇ}^{z}-1}$, in cylindrical coordinates, with r ranging from 0 to 10 and theta from 0 to $2\mathrm{\pi }$.

 > g := proc(z) local w; w := Re(z)*exp(Im(z)*I); w/(exp(w)-1) end proc:
 > $\mathrm{changecoords}\left(\mathrm{complexplot3d}\left(g,0..10+2\mathrm{π}I,\mathrm{axes}=\mathrm{boxed}\right),\mathrm{cylindrical}\right)$

The command to create the plot from the Plotting Guide is

 > $\mathrm{complexplot3d}\left(\mathrm{sec}\left(z\right),z=-2-2I..2+2I,\mathrm{grid}=\left[10,10\right]\right)$