"Imaginary Numbers Worksheet With Answer Key"

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Regents Exam Questions A2.N.7: Imaginary Numbers 1
Name: ________________________
www.jmap.org
A2.N.7: Imaginary Numbers 1: Simplify powers of i
1 Mrs. Donahue made up a game to help her class
99
7 When simplified, i
is equivalent to
learn about imaginary numbers. The winner will be
1)
1
the student whose expression is equivalent to i .
1
2)
Which expression will win the game?
3)
i
46
i
1)
4)
i
47
2)
i
48
3)
233
8 Which expression is equivalent to i
i
49
1)
1
4)
i
1
2)
3)
i
2 For any power of i, the imaginary unit, where b is a
 i
4)
4b  3
whole number, i
equals
1)
1
37
9 Which expression is equivalent to i
2)
i
1
1)
1
3)
1
 i
2)
4)
3)
i
 i
4)
25
3 The expression i
is equivalent to
1)
1
2
 3i
3
10 The expression 2i
1
is equivalent to
2)
2  3i
1)
3)
i
2  3i
 i
2)
4)
2  3i
3)
2  3i
4)
55
4 Which expression is equivalent to i
?
1)
1
27
 i
34
1
11 When simplified, i
is equal to
2)
1)
3)
i
i
 i
61
4)
2)
i
i  1
3)
i  1
4)
16
5 The value of i
is
1)
1
1
100
 i
101
 i
102
2)
12 The expression i
equals
3)
1)
1
i
i
 1
4)
2)
i
3)
4)
i
10
6 The expression i
is equivalent to
1)
1
13 If i is the imaginary unit, the expression
2)
i
1
8
 i
9
 i
10
 i
11
3)
is equivalent to
i
i
4)
1)
1
 1
2)
3)
i
4)
0
1
Regents Exam Questions A2.N.7: Imaginary Numbers 1
Name: ________________________
www.jmap.org
A2.N.7: Imaginary Numbers 1: Simplify powers of i
1 Mrs. Donahue made up a game to help her class
99
7 When simplified, i
is equivalent to
learn about imaginary numbers. The winner will be
1)
1
the student whose expression is equivalent to i .
1
2)
Which expression will win the game?
3)
i
46
i
1)
4)
i
47
2)
i
48
3)
233
8 Which expression is equivalent to i
i
49
1)
1
4)
i
1
2)
3)
i
2 For any power of i, the imaginary unit, where b is a
 i
4)
4b  3
whole number, i
equals
1)
1
37
9 Which expression is equivalent to i
2)
i
1
1)
1
3)
1
 i
2)
4)
3)
i
 i
4)
25
3 The expression i
is equivalent to
1)
1
2
 3i
3
10 The expression 2i
1
is equivalent to
2)
2  3i
1)
3)
i
2  3i
 i
2)
4)
2  3i
3)
2  3i
4)
55
4 Which expression is equivalent to i
?
1)
1
27
 i
34
1
11 When simplified, i
is equal to
2)
1)
3)
i
i
 i
61
4)
2)
i
i  1
3)
i  1
4)
16
5 The value of i
is
1)
1
1
100
 i
101
 i
102
2)
12 The expression i
equals
3)
1)
1
i
i
 1
4)
2)
i
3)
4)
i
10
6 The expression i
is equivalent to
1)
1
13 If i is the imaginary unit, the expression
2)
i
1
8
 i
9
 i
10
 i
11
3)
is equivalent to
i
i
4)
1)
1
 1
2)
3)
i
4)
0
1
Regents Exam Questions A2.N.7: Imaginary Numbers 1
Name: ________________________
www.jmap.org
16
 i
6
 2i
5
 i
13
2
 5i) is equivalent to
21 The expression 3i(2i
14 Expressed in simplest form, i
is
equivalent to
15  6i
1)
15  5i
1)
1
2)
1
15  5i
2)
3)
1  0i
3)
4)
i
i
4)
3
3
22 What is the value of (5i
)
?
99
 i
3
15 What is the value of i
?
125i
1)
1)
1
2)
125i
96
15i
3)
2)
i
i
3)
4)
15i
4)
0
23 If f(x)  x
2
3
, what is the value of f(i
) ?
3
 i
7
16 The product i
is
1)
1
1
1)
1
2)
1
2)
3)
i
i
3)
4)
i
i
4)
24 If f(x)  x
2
, what is the value of f(2i) ?
7
5
17 The product of i
and i
is equivalent to
2
1)
1)
1
2)
2
1
2)
4
3)
3)
i
4)
4
i
4)
25 If f(x)  x
3
 2x
2
, then f(i) is equivalent to
0
 i
1
 i
2
 i
3
 i
4
18 The expression i
is equal to
2  i
1)
1)
1
2  i
2)
1
2)
2  i
3)
3)
2  i
i
4)
i
4)
2
3
 2xi
12
26 The expression x(3i
)
is equivalent to
16
i
2x  27xi
1)
19 The expression
is equivalent to
3
7x
2)
i
25x
1)
1
3)
1
29x
2)
4)
3)
i
 i
4)
8
 yi
6
27 Express xi
in simplest form.
2
(2  i) is equivalent to
20 The expression i
28 Express 4xi  5yi
8
 6xi
3
 2yi
4
in simplest a  bi
2  i
1)
2  i
form.
2)
2  i
3)
2  i
4)
29 Determine the value of n in simplest form:
13
 i
18
 i
31
 n  0
i
2
ID: A
A2.N.7: Imaginary Numbers 1: Simplify powers of i
Answer Section
1 ANS: 2
REF: 060615b
2 ANS: 4
REF: 061615a2
3 ANS: 3
REF: 010705b
4 ANS: 4
REF: 010905b
5 ANS: 1
REF: 018631siii
6 ANS: 3
REF: 069527siii
7 ANS: 4
REF: 089830siii
8 ANS: 3
REF: 010334siii
9 ANS: 3
REF: 080327siii
10 ANS: 1
2
 3i
3
 2(1)  3(i)  2  3i
2i
REF: 081004a2
11 ANS: 3
REF: 080407b
12 ANS: 4
REF: 060819b
13 ANS: 4
REF: 060331siii
14 ANS: 4
REF: 080215b
15 ANS: 4
REF: 060315b
16 ANS: 2
REF: 088423siii
17 ANS: 1
REF: 061019a2
18 ANS: 2
REF: 060410b
19 ANS: 3
REF: 010518b
20 ANS: 2
REF: 069925siii
21 ANS: 1
REF: 080702b
22 ANS: 2
REF: 060224siii
23 ANS: 2
REF: 010034siii
24 ANS: 3
REF: 080128siii
25 ANS: 4
REF: 010415b
26 ANS: 3
6
)  x(2i
12
)  27x  2x  25x
x(27i
REF: 011620a2
27 ANS:
8
 yi
6
 x(1)  y(1)  x  y
xi
REF: 061533a2
28 ANS:
4xi  5yi
 6xi
 2yi
 4xi  5y  6xi  2y  7y  2xi
8
3
4
REF: 011433a2
1
ID: A
29 ANS:
13
 i
18
 i
31
 n  0
i
i  (1)  i  n  0
1  n  0
n  1
REF: 061228a2
2
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