Before working with complex numbers, you need to adjust the mode setting on your TI-83. Highlight a + bi on the seventh line as shown below.

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1 1 Arapahoe Community College MAT Graphing Calculator Techniques for Survey of Algebra TI-83 Graphing Calculator Workshop #10 Complex Numbers and Programming 1) Demonstrate how to enter and perform operations with complex numbers on the TI-83. 2) Demonstrate how to store and retrieve information in a program, 3) Illustrate how to delete a program from memory, 4) Show how to insert and delete lines in a program, 5) Show how to cut and paste lines in a program 6) Build a more elaborate quadratic formula function. Complex Numbers Before working with complex numbers, you need to adjust the mode setting on your TI-83. Highlight a + bi on the seventh line as shown below. The small letter i above the decimal point <9, 3> is used to represent 1. Complex numbers are generally written in the form a + bi where a and b are any real numbers. 1) Start with a clear Home Screen. 2) Enter ( 49) ( 4). Be sure to use the parentheses. Press. 3) You can also perform operations with complex numbers. Use. <9,3> to access the small i on the keyboard. Try these. a) (12-6i) + (3 + 2i) ans 15-4i b) (6-3i) - (4-8i) ans 2 + 5i

2 2 c) (5 + 2i) (3-5i) ans 25-19i d) (4-3i) / (4 + 3i) Frac ans 7/25 - (24/25)i 4) Perform these calculations and report your results. a) (4-2i) + ( 3-5i) ans b) + i i ans c) ( 4 4 ) ans d) (2-3i) ( 4 4 ) ans e) (6-3i) / (4 + 2i) ans Storing Information in a Program 1) Press,<3, 3>, to NEW, and press. 2) Type in the name of your program. Notice that the calculator is in Alpha lock mode. Type in INFO. 3) Notice program lines start with : Character. 4) Use the arrow keys and the enter key to enter the following program. Spaces are entered as. 5) Press to return to the Home Screen. Retrieving Information from a Program You will now go back to the program you just entered to recall the information stored there. 1) Press. 2) Arrow over to EDIT and arrow down to INFO. Press. 3) Your program should now be on the screen. You can use all the arrow keys to move around this program.

3 3 Deleting a line from a Program You will now remove unwanted lines. 1) Use the arrow keys to move the cursor somewhere in the first "THIS IS INFO 5" line. 2) Press. 3) What happens? Adding a Line to a Program You will now add a line to your program. 1) Use the arrow keys to move the cursor at the beginning of the "THIS IS INFO 5" line. 2) Press. 3) What happens? 4) Add the following line to your program. Deleting a Program Suppose you are finished with your information program and want to remove it from the memory of your calculator. This is useful as your calculator memory becomes full. 1) Press to return to the Home Screen. 2) To access the memory functions, press and to access Mem Mgm t/del menu option. 3) Press for Program or arrow down to it and press. 4) Arrow to INFO and be sure that the small triangle pointer is next to it. Press. The program has been deleted which frees calculator RAM.

4 4 A Quadratic Formula Program You will now create a quadratic formula program. Running a Program 1) Create a new program named QUADRATC. (8 letter limit) 2) Press to NEW, press. Type QUADRATC then press. 3) Press and to I/O for Input/Output. Press for Input or press. 4) Enter the following program. Disp is below Input on the I/O menu. " is accessed by pressing. Press for =. :Input ("A=",A) :Input ("B=",B) :Input ("C=",C) :Disp "B 2-4 A C=" :Disp B 2-4 A C :Disp "X1=" :Disp (-B + (B4 A C))/(2 A) :Disp "X2=" :Disp (-B - (B4 A C))/(2 A) 5) Press to return to the Home Screen. You can execute a program from the Home Screen by pressing and using the arrows to move down to its name and pressing. 1) Call up your QUADTRTC program. 2) Press. The program will now prompt you to enter the values for A, B and C. 3) If we wished to find the solutions for x 2 + 4x - 5 = 0, we would input A = 1, B = 4 and C = -5.

5 5 4) Press. The screen now shows you the value of the discriminant as well as the two roots. It says "done" indicating that the program has finished running. 5) Find the value of the discriminant as well as the solutions to the following equations: (you can run the quadratic program again by simply pressing ) x 2 + 4x - 10 = 0 B 2-4AC =, solutions x =, x = x 2 + 4x - 7 = 0 B 2-4AC =, solutions x =, x = x 2 + 4x - 4 = 0 B 2-4AC =, solutions x =, x = x 2 + 4x - 3 = 0 B 2-4AC =, solutions x =, x = x 2 + 4x = 0 B 2-4AC =, solutions x =, x = x 2 + 4x + 2 = 0 B 2-4AC =, solutions x =, x = x 2 + 4x + 4 = 0 B 2-4AC =, solutions x =, x =

6 6 x 2 + 4x + 5 = 0 B 2-4AC =, solutions x =, x = x 2 + 4x + 8 = 0 B 2-4AC =, solutions x =, x =