Station 1: Operations with Complex Numbers- Addition & Subtraction
Race your group to complete the following additional and subtraction
problems. Show all work in your packet. When you have finished, check your
answers. Record the winner in packet next to the trophy.
1. (1 + 3i) + (2 + 5i)
2. (3 + 7i) + (10 – 11i)
3. (18+3i) + (4+2i)
4. (16 + 2i) + (10 + i)
5. (4i – 7) + (12 – 4i)
6. (a + gi) + (2a + 3gi)
7. (7i – 8) – (18 – 2i)
8. (3i + 2) – (3i – 2)
9. (10 – 5i) – (3 + 2i)
10. (2 + 10i) – (6 – 7i)
Station 2: Powers of i
Work with your group to solve the following problems. Show all your work.
Check the hints for help.
Evaluate:
1. i1 =
2. i2 =
3. i3 =
4. i4 =
5. i5 =
6. i6 =
7. i7 =
8. i8=
9. What is the pattern? As a group, make a conjecture about simplifying
powers of i. Raise your hand, and check in with Mrs. Yorke before
proceeding with the next set of problems.
10. i13
11. i20
12. i18
13. i27
14. i147
15. i 71  i 49
16. i 68  i 72  i 76  i 80
17. i 9
18. i 27
Station 3: Operations with Complex Numbers-Multiplication
Work with your group to solve the following problems. Show all your work.
Use your calculator to check.
Select 4 Problems from 1 – 8 and complete 9-12.
1. (1 + 3i)(2 + 5i)
2. (3 + 7i)( 4 + 2i)
3. (-1 + 2i)(3 – 2i)
1
4


4.   2i (10  i )
5. (2i – 3)4i
6. (3 – i)( 4 + i)
7. (8 + 3i)(4 – 5i)
8. (10 – 2i3)(4 + i)
9. (9 + 2i)(9 – 2i)
10. (5 + 3i)(5 – 3i)
11. (6 – 3i) (6 + 3i)
12. In problems, 9, 10 and 11, you multiplied complex conjugates, what
conjecture can you make about multiplying complex conjugates?
Station 4: Operations with Complex Numbers-Division
Work with your group to simplify one of problems #1-3 and three of problems
#4-8. If needed, identify the conjugate c then simplify. Show all your work in
your packet. Check the hints folder for help on how to simplify division
problems.
1.
3  2i
 6i
2.
4  3i
3i
3.
5  2i
 2i
4.
3  2i
3  2i
5.
7  3i
7  3i
6.
8  3i
2i
7.
6  2i
5  3i
8.
3i
4  2i
Station 5: Operations with Complex Numbers-Simplifying I
Working with your group, select the appropriate number of problems for the
section and simplify. State your answer in terms of i. Show all your work. Use
your calculator to check.
I. Select 4 of the following 8 problems to answer.
1.
2
2.
3
6.   16
5.   9
3.
 36
4.
 25
7.
 128
8.
 12
II. Select 2 of the following 4 problems to answer.
9.
9
16
10.
 25
4
12.   75
11.   80
III. Select 2 of the following 4 problems to answer.
14.  12i  (3)
13. 23i  4
 3  4i
15.
IV. Select 4 of the following 8 problems to answer.
17.
2  3
18.
20.   3   15
19.   2   18
21.
 3   15

23.  10   10
5 3
22.

 10   2

24.   7   7

16.
 5  6i
Station 6: Operations with Complex Numbers-Simplifying II
*Must Complete Stations 4 and 5 First!!!
Work with your group to simplify four of the following problems. State your
answer in terms of a + bi. Show all your work.
1
4
1. 8  
2.
 16  3
3.
9 2
4.
 25  16  4
5.


4
3 9


1


6. 2  4 

3  4 


7. 3   4 3   4
8.
1
4  1


2  2  36
3 4
Station 7: Complex Numbers: Solving Equations
Work with your group to solve the following problems. State your answer in
terms of a + bi or bi. Show all your work. Check the hints for help.
Select 3 problems from 1 -6 and Select 3 problems from 7-12.
1. x2 + 64 = 0
2. 3x2 + 27 = 0
3. 4x2 + 1 = 0
4. x2 = 11
5. 2x2 + 5 = 31
6. 3x2 = 16
7. x2 + 2x + 5 = 0
8. x2 + 2x  10 = 0
9. 2x2  3x + 5 = 0
10. 4x2 + 6x  3 = 0
11. 3x2 + 2x + 5 = 0
12. 2x2  2x + 7 = 0
Station 8: Graphing in the Complex Number Plane
Work with your group to solve the following problems. Select 4 of the
following to graph on the complex number plane provided. Then determine its
distance from the origin.
1. 4 + 9i
2. 6 + 2i
3. -3 + 5i
4. 5 – 7i
5. 7 – 10i
6. -6 + i
7. 2 + 7i
8. -1 – 4i