Polar Coordinates And Complex Numbers Worksheets With Answers - Math 611b Page 16
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50Simplifying Complex Numbers Worksheet (9.5)
1. Read pages 41 and 42 in the workbook.
2. Describe how to simplify any integral power of i.
3. Draw a Venn diagram to show the relationship between real, pure imaginary and complex numbers.
4. Explain why it is useful to multiply by the conjugate of the denominator over itself when simplifying a
fraction containing complex numbers.
5. Write a quadratic equation that has two complex conjugate solutions.
6. Simplify.
!6
c) (2 + 3i) + ( ! 6 + i)
d) (2.3 + 4.1i) ! ( ! 1.2 ! 6.3i)
10
2
a) i
b) i
+ i
e) (2 + 4i) + ( ! 1 + 5i)
f) ( ! 2 ! i)
2
6
g) i
!5
k) (3 + 2i) + ( ! 4 + 6i)
19
1776
9
h) i
i) i
j) i
+ i
l) (7 ! 4i) + (2 ! 3i)
m) (1/2 + i) ! (2 ! i)
n) ( ! 3 ! i) ! (4 ! 5i)
+
− −
2
(
1
7
i
)(
2
5
i
)
o) (2 + i)(4 + 3i)
p) (1 + 4i)
q)
+
−
−
2
i
3
2
i
5
i
+
−
− +
−
(
2
3
)(
1
12
)
r)
s)
t)
u)
+
− −
+
1
2
i
4
i
5
i
7. Write a quadratic equation with solutions i and ! i.
8. Write a quadratic equation with solutions 2 + i and 2 ! i.
9. Simplify.
1
+
3
i
2
a) (2 ! i)(3 + 2i)(1 ! 4i)
b) ( ! 1 ! 3i)(2 + 2i)(1 ! 2i)
c)
−
1
2
i
−
+
+
2
2
2
i
3
i
(
1
i
)
d)
e)
f)
+
− +
+
2
2
(
2
i
)
(
3
2
i
)
3
6
i
16
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education