170 Chapter 10: 3D Graphing
10_3D.DOC TI-89/TI-92 Plus: 3D Graphing (English) Susan Gullord Revised: 02/23/01 11:00 AM Printed: 02/23/01 4:22 PM Page 170 of 2210_3D.DOC TI-89/TI-92 Plus: 3D Graphing (English) Susan Gullord Revised: 02/23/01 11:00 AM Printed: 02/23/01 4:22 PM Page 170 of 22
In this example, let f(x)=x3+1. By substituting the general complex
form x+yi for x, you can express the complex surface equation as
z(x,y)=abs((x+yùi)3+1).
1. Use 3to set Graph=3D.
2. Press ¥#
, and define the
equation:
z1(x,y)=abs((x+yùi)^3+1)
3. Press ¥$
, and set
the Window variables as
shown.
4. Display the Graph Formats
dialog box:
TI-89: ¥Í
TI-92 Plus: ¥F
Turn on the axes, set
Style = CONTOUR LEVELS,
and return to the Window
editor.
5. Press ¥%to graph the equation.
It will take awhile to evaluate the graph; so be patient. When the
graph is displayed, the complex modulus surface touches the
xy plane at exactly the complex zeros of the polynomial:
ë1, 1
2 + 3
2 i , and 1
2 ì3
2 i
6. Press …, and move the
trace cursor to the zero in
the fourth quadrant.
The coordinates let you
estimate .428ì.857 i as
the zero.
7. Press N. Then use the
cursor keys to animate the
graph and view it from
different eye angles.
Example: Contours of a Complex Modulus Surface
The complex modulus surface given by z(a,b) = abs(f(a+bi))
shows all the complex zeros of any polynomial y=f(x).
Example
Note: For more accurate
estimates, increase the
xgrid
and
ygrid
Window
variables. However, this
increases the graph
evaluation time.
Tip: When you animate the
graph, the screen changes
to normal view. Use
p
to
toggle between normal and
expanded views.
The zero is precise when z=0.
This example shows eyeq=70,
eyef=70, and eyeψ=0.