Visualizing Complex Zeros Of A Cubic Polynomial - Texas Instruments TI-89 Manual Book

Visualizing Complex Zeros of a Cubic Polynomial

Visualizing Complex
Roots
Hint: Move the cursor into
the history area to highlight
the last answer and press
¸ , to copy it to the entry
line.
Note: The absolute value of
a function forces any roots
to visually just touch rather
than cross the x axis.
Likewise, the absolute value
of a function of two variables
will force any roots to
visually just touch the xy
plane.
Note: The graph of z1(x,y)
will be the modulus surface.
402 Chapter 23: Activities
This activity describes graphing the complex zeros of a cubic
polynomial. Detailed information about the steps used in this
example can be found in Chapter 3: Symbolic Manipulation
and Chapter 10: 3D Graphing.
Perform the following steps to expand the cubic polynomial
i i , find the absolute value of the function, graph the
(xì 1)(xì )(x+ )
modulus surface, and use the
surface.
1. On the Home screen, use the
function to expand
expand()
the cubic expression
ì i
i and see the first
(xì 1)(x ) (x+ )
polynomial.
2. Copy and paste the last answer
to the entry line and store it in
the function .
f(x)
3. Use the function to find
abs()
the absolute value of
(This calculation may take
about 2 minutes.)
4. Copy and paste the last answer
to the entry line and store it in
the function
z1(x,y)
5. Set the unit to 3D graph mode,
turn on the axes for graph
format, and set the Window
variables to:
eye= [20,70,0]
x= [ë 2,2,20]
y= [ë 2,2,20]
z= [ë 1,2]
ncontour= [5]
Trace tool to explore the modulus
f(x+y i ) .
.