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
z
≤1 and 0≤ Im
z
≤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) = , 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.
Plot 2D + Conformal
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
F(z)
≤4 and -3≤ Im
F(z)
≤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.
Plot 2D + Conformal
dtbpF3in2.0003in0pt