Download Complex Numbers

Name: ______________________ Class: _________________ Date: _________
Complex Numbers
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Express in the form a + bi, where a and b are real numbers.
8 ( cos
____
!
+ isin
4
4
)
a. 4 3 + 4 i
b. 8 2 + 8 2 i
c.
2 +4 2i
d. 4 2 " 4 2 i
e. 4 2 + 4 2 i
2. Express in the form a + bi, where a and b are real numbers.
10 cis( tan
____
!
"1
3)
a. 3 + 3i
b. 1 + 3i
c. 10 " 10i
d. 1 " 3i
e. 3 " 3i
3. Express the complex number in trigonometric form with 0 # $ # 2 !.
" 5 " 5i
a.
"5
2 cis
b.
10 cis
5!
4
c.
5
d.
5 cis
e.
5
2 cis
5!
4
2 cis
5!
4
!
4
5!
4
1
ID: N
Name: ______________________
____
ID: N
4. Use trigonometric forms to find z 1 z 2 and
z1
z2
z 1 = 2i, z 2 = " 3i
____
a.
z 1 z 2 = "6,
b.
z 1 z 2 = 6,
c.
z 1 z 2 = "6,
d.
z 1 z 2 = 6,
e.
z 1 z 2 = "6,
z1
z2
z1
z2
="
z1
z2
z1
z2
="
=
z1
z2
16
9
2
3
="
4
3
2
3
=
5
7
5. Find the solutions of the equation.
3
x + 27i = 0
a.
"3 i, "
b.
i,
c.
3 i,
d.
"3 i, "
e.
3 i,
3
3 3i
3 3i
3
3
+
," "
2
2
2
2
3
"
2
3
3
2
3
3 3
3i
3i
,"
"
2
2
2
"
3
2
3 3
3i
3i
,"
"
2
2
2
+
3 3
3i
3i
,"
"
2
2
2
3 3i 3
3 3i
3
+
, "
2
2
2
2
2
.
Name: ______________________
____
ID: N
6. Use trigonometric forms to find z 1 z 2 and
z1
z2
z 1 = "4 +4i, z 2 = 4 + 4i
____
z1
a.
z 1 z 2 = 32,
b.
z 1 z 2 = 32,
c.
z 1 z 2 = "32,
d.
z 1 z 2 = "32,
e.
z 1 z 2 = "32,
="1
z2
z1
=1
z2
z1
z2
z1
z2
z1
z2
= 32i
= "32i
= i
7. Find the solutions of the equation.
4
x " 81 = 0
____
a. 3, "3, 3 i, "3 i
b. 6 i, "6 i
c. 6, "6, 6 i, "6 i
d. 6 , "6 i
e. 3, "3
8. Find the three cube roots of "27i.
3 " 3 i, 3
a.
6 i, 3
b.
3 i,
c.
3 i, "
d.
6 i, "3
e.
3 i, "
3
3
"
2
3
2
3
3i 3 3
3i
,
+
2
2
2
"
3i 3 2
3i
,
"
2
3
2
3 " 3 i, 3
3
3
2
3 + 3i
"
3 " 3i
3i 3 3
3i
,
"
2
2
2
3
.
Name: ______________________
____
ID: N
9. Find the absolute value.
| 5 " 12i|
a.
b.
c.
d.
e.
____
10. Find the two square roots of 81 + 81
a.
9
6
"
9
c.
"
9
e.
+
2
b.
d.
____
169
13
5
7
12
6
6
"
2
"
+
2
6
9
2
"
2
9
9
6
2
2i 9
,
9
2
9
2
9
2i 9
,
2i
9
6
2
,"
+
6
2
6
2
9
9
"
2
2i 9
,
2
,
6
6
2
9
3 i.
2i
2
+
+
"
9
2i
2
9
2i
2
9
2i
2
2i
2
11. Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are
real numbers.
ÊÁÁ
2
2
ÁÁÁ
ÁÁÁÁ " 2 + 2
Ë
2
"
2
a.
b.
c.
2
"
2
1
i
" "
2
2
"
2
+
2
d.
e.
"
2
+
2
ˆ˜˜ 23
˜
i ˜˜˜˜
˜˜
¯
2i
2
2i
2
2i
2
2i
2
4
Name: ______________________
____
ID: N
12. Express the complex number in trigonometric form with 0 # $ # 2 !.
9 + 8i
a.
145 cis( tan
b.
145 cis( tan
c.
d.
e.
____
145
)
8
)
9
"1 8
145 cis( tan
)
9
8
145 cis
9
145 cis
!
2
13. Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are
real numbers.
(1 "
____
8
"1
3 i)
12
a. -4,096i
b. -2,048i
c. -2,048
d. 2,048i
e. 12
14. Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are
real numbers.
( 2 + 2i)
a.
b.
c.
d.
e.
5
128 + 128i
32 + 32i
" 128 + 128i
" 128 " 128i
128 " 128i
5
ID: N
Complex Numbers
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
E
B
E
B
C
E
A
E
B
B
B
C
E
D
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
MSC:
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MSC:
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Complex Numbers [Answer Strip]
B
_____
E
_____
4.
E
_____
ID: N
B
_____
9.
C
_____
12.
6.
1.
B
_____
10.
E
_____
13.
B
_____
2.
C
_____
5.
A
_____
7.
B
_____
11.
D
_____
14.
E
_____
3.
E
_____
8.