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Texas Instruments TI-89 User Manual - Page 766

Visualizing Complex Zeros of a Cubic Polynomial, Optional Exercise, Visualizing Complex Roots

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Optional Exercise Assuming the same initial velocity of 95 feet per second, find the angle that the ball should be hit to achieve the greatest distance. Visualizing Complex Zeros of a Cubic Polynomial This activity describes graphing the complex zeros of a cubic polynomial. Visualizing Complex Roots Perform the following steps to expand the cubic polynomial (xN1)(xNi)(x+i), find the absolute value of the function, graph the modulus surface, and use the Trace tool to explore the modulus surface. 1. On the Home screen, use the expand( ) function to expand the cubic expression (xN1)(xNi)(x+i) and see the first polynomial. 2. Copy and paste the last answer to the entry line and store it in the function f(x). Note: Move the cursor into the history area to highlight the last answer and press ¸, to copy it to the entry line. Activities 766

Section	Page
TI-89 Titanium Graphing Calculator	1
Getting Started	4
Initial start-up	4
TI-89 Titanium keys	9
Mode settings	17
Using the Catalog to access commands	21
Calculator Home screen	24
Working with Apps	28
Checking status information	38
Turning off the Apps desktop	39
Using the clock	40
Using menus	49
Using split screens	59
Managing Apps and operating system (OS) versions	65
Connecting your TI-89 Titanium to other devices	67
Batteries	69
Previews	73
Performing Computations	73
Symbolic Manipulation	82
Constants and Measurement Units	84
Basic Function Graphing I	86
Basic Function Graphing II	89
Basic Function Graphing III	92
Parametric Graphing	94
Polar Graphing	96
Sequence Graphing	98
3D Graphing	101
Differential Equation Graphing	105
Additional Graphing Topics	110
Tables	112
Split Screens	114
Data/Matrix Editor	117
Statistics and Data Plots	119
Programming	128
Text Operations	131
Numeric Solver	133
Number Bases	136
Memory and Variable Management	138
Operating the Calculator	145
Turning the Calculator On and Off	145
Setting the Display Contrast	147
The TI-89 Titanium Keyboard	148
Modifier Keys	150
Entering Alphabetic Characters	153
Entering Numbers	156
Entering Expressions and Instructions	158
Formats of Displayed Results	165
Editing an Expression in the Entry Line	171
Menus	175
Selecting an Application	181
Setting Modes	185
Using the Clean Up Menu to Start a New Problem	189
Using the Catalog Dialog Box	191
Storing and Recalling Variable Values	197
Status Line Indicators in the Display	201
Calculator Home Screen	205
Calculator Home Screen	205
Saving the Calculator Home Screen Entries as a Text Editor Script	210
Cutting, Copying, and Pasting Information	212
Reusing a Previous Entry or the Last Answer	217
Auto-Pasting an Entry or Answer from the History Area	221
Creating and Evaluating User-Defined Functions	223
If an Entry or Answer Is “Too Big”	228
Using the Custom Menu	230
Finding the Software Version and ID Number	233
Symbolic Manipulation	235
Using Undefined or Defined Variables	235
Using Exact, Approximate, and Auto Modes	240
Automatic Simplification	244
Delayed Simplification for Certain Built-In Functions	247
Substituting Values and Setting Constraints	249
Overview of the Algebra Menu	255
Common Algebraic Operations	258
Overview of the Calc Menu	265
Common Calculus Operations	267
User-Defined Functions and Symbolic Manipulation	269
If You Get an Out-of-Memory Error	273
Special Constants Used in Symbolic Manipulation	275
Constants and Measurement Units	279
Entering Constants or Units	279
Converting from One Unit to Another	283
Setting the Default Units for Displayed Results	287
Creating Your Own User-Defined Units	290
List of Pre-Defined Constants and Units	293
Basic Function Graphing	302
Overview of Steps in Graphing Functions	302
Setting the Graph Mode	304
Defining Functions for Graphing	305
Selecting Functions to Graph	309
Setting the Display Style for a Function	311
Defining the Viewing Window	313
Changing the Graph Format	315
Graphing the Selected Functions	317
Displaying Coordinates with the Free-Moving Cursor	319
Tracing a Function	321
Using Zooms to Explore a Graph	325
Using Math Tools to Analyze Functions	330
Polar Graphing	340
Overview of Steps in Graphing Polar Equations	340
Differences in Polar and Function Graphing	342
Parametric Graphing	347
Overview of Steps in Graphing Parametric Equations	347
Differences in Parametric and Function Graphing	349
Sequence Graphing	354
Overview of Steps in Graphing Sequences	354
Differences in Sequence and Function Graphing	356
Setting Axes for Time, Web, or Custom Plots	363
Using Web Plots	364
Using Custom Plots	370
Using a Sequence to Generate a Table	373
3D Graphing	375
Overview of Steps in Graphing 3D Equations	375
Differences in 3D and Function Graphing	377
Moving the Cursor in 3D	382
Rotating and/or Elevating the Viewing Angle	386
Animating a 3D Graph Interactively	391
Changing the Axes and Style Formats	393
Contour Plots	396
Example: Contours of a Complex Modulus Surface	402
Implicit Plots	404
Example: Implicit Plot of a More Complicated Equation	407
Differential Equation Graphing	410
Overview of Steps in Graphing Differential Equations	410
Differences in Diff Equations and Function Graphing	412
Setting the Initial Conditions	421
Defining a System for Higher-Order Equations	425
Example of a 2nd-Order Equation	427
Example of a 3rd-Order Equation	431
Setting Axes for Time or Custom Plots	434
Example of Time and Custom Axes	435
Example Comparison of RK and Euler	439
Example of the deSolve( ) Function	444
Troubleshooting with the Fields Graph Format	447
Tables	454
Overview of Steps in Generating a Table	454
Setting Up the Table Parameters	455
Displaying an Automatic Table	459
Building a Manual (Ask) Table	464
Additional Graphing Topics	469
Collecting Data Points from a Graph	469
Graphing a Function Defined on the Home Screen	471
Graphing a Piecewise Defined Function	475
Graphing a Family of Curves	479
Using the Two-Graph Mode	482
Drawing a Function or Inverse on a Graph	487
Drawing a Line, Circle, or Text Label on a Graph	489
Saving and Opening a Picture of a Graph	497
Animating a Series of Graph Pictures	500
Saving and Opening a Graph Database	503
Split Screens	506
Setting and Exiting the Split Screen Mode	506
Selecting the Active Application	512
Data/Matrix Editor	516
Overview of List, Data, and Matrix Variables	516
Starting a Data/Matrix Editor Session	520
Entering and Viewing Cell Values	523
Defining a Column Header with an Expression	528
Using Shift and CumSum Functions in a Column Header	533
Sorting Columns	535
Saving a Copy of a List, Data, or Matrix Variable	537
Statistics and Data Plots	540
Overview of Steps in Statistical Analysis	540
Performing a Statistical Calculation	541
Statistical Calculation Types	545
Statistical Variables	548
Defining a Statistical Plot	551
Statistical Plot Types	554
Using the Y= Editor with Stat Plots	558
Graphing and Tracing a Defined Stat Plot	560
Using Frequencies and Categories	563
If You Have a CBL 2™ or CBR™	568
Programming	572
Running an Existing Program	572
Starting a Program Editor Session	576
Overview of Entering a Program	579
Overview of Entering a Function	585
Calling One Program from Another	590
Using Variables in a Program	593
Using Local Variables in Functions or Programs	597
String Operations	600
Conditional Tests	603
Using If, Lbl, and Goto to Control Program Flow	606
Using Loops to Repeat a Group of Commands	610
Configuring the TI-89 Titanium	616
Getting Input from the User and Displaying Output	618
Creating a Custom Menu	622
Creating a Table or Graph	627
Drawing on the Graph Screen	629
Accessing Another TI-89 Titanium, a CBL 2, or a CBR	633
Debugging Programs and Handling Errors	635
Example: Using Alternative Approaches	637
Assembly-Language Programs	641
Text Editor	645
Starting a Text Editor Session	645
Entering and Editing Text	648
Entering Special Characters	655
Entering and Executing a Command Script	661
Numeric Solver	666
Displaying the Solver and Entering an Equation	666
Defining the Known Variables	670
Solving for the Unknown Variable	674
Graphing the Solution	675
Number Bases	680
Entering and Converting Number Bases	680
Performing Math Operations with Hex or Bin Numbers	682
Comparing or Manipulating Bits	684
Memory and Variable Management	689
Checking and Resetting Memory	689
Displaying the VAR-LINK Screen	691
Displaying Information about Variables on the Home Screen	694
Pasting a Variable Name to an Application	705
Archiving and Unarchiving a Variable	707
If a Garbage Collection Message Is Displayed	709
Memory Error When Accessing an Archived Variable	713
Connectivity	716
Connecting Two Units	716
Transmitting Variables, Flash Applications, and Folders	719
Transmitting Variables under Program Control	727
Upgrading the Operating System (OS)	731
Collecting and Transmitting ID Lists	736
Compatibility among the TI-89 Titanium, Voyage™ 200, TI-89, and TI-92 Plus	738
Activities	741
Analyzing the Pole-Corner Problem	741
Deriving the Quadratic Formula	743
Exploring a Matrix	746
Exploring cos(x) = sin(x)	748
Finding Minimum Surface Area of a Parallelepiped	750
Running a Tutorial Script Using the Text Editor	752
Decomposing a Rational Function	754
Studying Statistics: Filtering Data by Categories	757
CBL 2™ Program for the TI-89 Titanium	761
Studying the Flight of a Hit Baseball	763
Visualizing Complex Zeros of a Cubic Polynomial	766
Solving a Standard Annuity Problem	769
Computing the Time-Value-of-Money	771
Finding Rational, Real, and Complex Factors	773
Simulation of Sampling without Replacement	775
Using Vectors to Determine Velocity	776
Appendix A: Functions and Instructions	914
TI-89 Titanium / Voyage™ 200 Error Messages	920
TI-89 Titanium / Voyage™ 200 Character Codes	938
Complex Numbers and Degree Mode	938
Accuracy Information	939
EOS (Equation Operating System) Hierarchy	941
Regression Formulas	952
setGraph( )	958
setTable( )	961
Appendix D: Service and Warranty Information	962
Texas Instruments Support and Service	962
Texas Instruments (TI) Warranty Information	963
TI-89 Titanium Shortcut Keys	967
Voyage™ 200 Shortcut Keys	971