Conformal Plots

A conformal plot of a complex function F(z) is the image of a two-dimensional rectangular grid of horizontal and vertical line segments. The default is an 11 by 11 grid, with each of the intervals ≤ Re $\left(\vphantom{ z}\right.$z$\left.\vphantom{ z}\right)$≤1 and 0≤ Im $\left(\vphantom{ z}\right.$z$\left.\vphantom{ z}\right)$≤1 subdivided into 10 equal subintervals. If F(z) is analytic, then it preserves angles at every point at which F(z)≠ 0; hence, the image is a grid composed of two families of curves that intersect at right angles.

To create a conformal plot of F(z) = ${\dfrac{{z-1}}{{z+1}}}$, put the insertion point in the expression, and choose Conformal from the Plot 2D submenu. The number of grid lines and the view can be changed in the Plot Properties tabbed dialogs.

$\blacktriangleright$ Plot 2D + Conformal

${\dfrac{{z-1}}{{z+1}}}$

dtbpF3in2.0003in0pt In the following example, Re(z) and Im(z) both range from -3 to 3, the View Intervals are set at -2≤ Re $\left(\vphantom{
F(z)}\right.$F(z)$\left.\vphantom{
F(z)}\right)$≤4 and -3≤ Im $\left(\vphantom{
F(z)}\right.$F(z)$\left.\vphantom{
F(z)}\right)$≤3, the Grid Size has been increased to 40 by 40, and Samples per Horizontal Grid Line and Samples per Vertical Grid Line have both been increased to 60.


$\blacktriangleright$ Plot 2D + Conformal

${\dfrac{{z-1}}{{z+1}}}$dtbpF3in2.0003in0pt