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15 pts
Alg II - Trig
Chapter 1 Enrichment – Go to Schoolwires to access this file.
Rationale:
You have learned about a new number system – the Complex
Number System. You have performed many operations with these
numbers and simplified many expression. It is now time to take a visual
look at complex numbers.
Task: Go through the following steps to learn more. Use the provided worksheet to
record your answers.
Part I - Exploring Graphing on the Argand Plane
Step 1:
Go to http://www.regentsprep.org/Regents/math/algtrig/ATO6/cgraphlesson.htm
and read about graphing complex numbers (including add/subtract complex # on the
plane).
Step 2:
Go to http://www.regentsprep.org/Regents/math/algtrig/ATO6/cgraphprac.htm.
Work through the given problems INDEPENDETLY on a piece of graph paper and
check your answers with the website.
Step 3: Complete the following on your worksheet.
Graph the following on a clean piece of graph paper.
1) (6 + i) + (4 + 4i)
2) (-5 + 2i) + (-1 – 3i)
3) (7 – 3i) + (-2 – i)
4) (8 - 4i) + (2 - 6i)
Exploring Absolute Value of Complex Numbers
Step 4:
Learn about finding the absolute value of Complex Numbers by going to:
http://www.regentsprep.org/Regents/math/algtrig/ATO6/absvlecomlesson.htm
Now go to the link below & follow directions for practice finding the absolute value
of complex numbers.
http://www.classzone.com/cz/books/algebra_2_2007_na/book_home.htm?state=NJ
Click on Animations
Select Ch 4 – 6 on the left
Select Chapter 4: Find Absolute Values of Complex Numbers
Work through a minimum of 5 different problems. If you are not confident do
more!!
While working… open a word document…You MUST do a screen
capture (shift + apple + 3) for each problem that you complete. See
figure below.
The picture will save to your desktop… Drag it into WORD.
Step 5:
Now complete the following problems on your worksheet. Show all work!
1) | 5 + 12i |
2) |-3 + 9i |
3) | 4 – 10i |
4) |-8 – 2i |
Step 6: Record the following answers on your worksheet.
A) List ten complex numbers that have the same absolute value.
B) Plot these numbers on a complex plane prepared on graph paper.
C) Determine what geometric figure contains ALL of the points that
represent the absolute value.
Part II - Exploring Complex Numbers on the Graphing Calculator
So did you know that you are able to perform operations with Complex Numbers on
your graphing calculator? Pick up your graphing calculator and now learn how it can be
done. However, you may find that it is faster to do the calculations by hand!
Step 1:
Go to www.mathbits.com and find the box for “Finding Your Way Around Your Graphing
Calculator”. Click on the TI-83+/TI-84+ Calculator link, then go to Algebra II and click
on Complex Numbers, or go to:
http://www.mathbits.com/MathBits/TISection/Algebra2/complexgc.htm)
Read about using your graphing calculator to perform operations with complex numbers.
Step 2:
Use your graphing calculator to perform the following operations. Record the following
answers on your worksheet.
NO WORK NEEDS TO BE SHOWN!
1) (123 – 15i) + (-114 + 22i)
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2) (19 + 44i) – (32 – 16i)
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3) (51 – 27i)(11 – 35i)
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4)
24 - 16i
32 + 6i
5) i259
6) What does your answer for #5 mean?
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