Download Complex Numbers

Name:
Date:
Advanced Math
Complex Numbers – Chapter 2.5
Solve each of the following for x. Decide whether each solution is real rational, real
irrational, or imaginary.
1.
x 2 - 2x + 1 = 0
2.
x 2 + 3x + 2 = 0
3.
x 2 + 3x - 2 = 0
4.
x2 - x - 1 = 0
5.
x 2 - 25 = 0
6.
x2 - 9 = 0
7.
x 2 + 25 = 0
8.
x2 + 9 = 0
1
Name:
Date:
Advanced Math
Imaginary Numbers
Defined
Examples
Powers of i
Complex Numbers
a + bi

Real Numbers

Imaginary Numbers

Pure Imaginary Numbers
2
Name:
Date:
Advanced Math
Operations with Complex Numbers

Addition

Subtraction

Multiplication

Division
Complex Conjugates ( z )
3
Name:
Date:
Advanced Math
Imaginary Numbers and the Powers of i
For problems 1-20, simplify and express your answer in terms of i.
1. i 5
2. i 7
3. i 55
4. i 25
5. i 62
6. i 74
7. i 300
8. i 180
9. i 0
10. i -2
11. i -7
12. i -25
13. i -38
14. i -54
15.
- 16
16.
- 25
17.
- 18
18.
- 48
19.
-7
20.
-3
4
Name:
Date:
Advanced Math
Practice
Simplify each expression
1.
- 4 + - 16 + - 1
-1 - 9
3.
4.
- 12
5.
6.
-3
7. (4 - 3i ) + (- 6 + 8i )
9. 4(3 + 5i ) - 2(2 - 6i )
11. (6 - i )(6 + i )
(
2.
)(
13. 5 + i 5 5 - i 5
15. (8 + 3i )(2 - 5i )
- 49 + - 9 + - 36
-2 -5
- 25
- 50
8. (7 - 8i ) - (6 + 2i )
10.
1
2
(7 - 2i ) + (5 - 5i )
6
3
12. (7 + 3i )(7 - 3i )
)
14.
( 3 + 4i 2 )( 3 - 4i 2 )
16. (5 - 2i )(- 1 + 3i )
5
Name:
Date:
2
17. (4 - 5i )
Write each expression in the form a + bi
1
19.
2 + 5i
21.
23.
25.
5+i
5-i
3+i 2
Advanced Math
2
18. (4 + 7i )
20.
1
4 - 3i
22.
3 - 2i
3 + 2i
2+i 5
7-i 2
24.
5
i
i 2 + 2i 3
26.
i
3-i 5
27. i + i 2 + i 3 + i 4 + i 5
28. i 46 + i 47
29. i -3
30. i -6
6
Name:
Date:
31. i -35
Advanced Math
32. (i n )
4
33.
Find real number x and y such that (2 x + y)+ (3 - 5x)i = 1 - 7i .
34.
Find real number x and y such that (3x - 4 y)+ (6x + 2 y)i = 5i .
35.
Show that the sum of a + bi and its conjugate is a real number.
36.
Show that the product a + bi and its conjugate is a nonnegative real number.
37a.
How could you show that 79 is a square root of 6421 without using a calculator?
37b.
How could you show that 3 – i is a square root of 8 - 6i?
38.
Show that 4-3i is a square root of 7-24i.
7