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Real And Complex Numbers Flashcards

1
Q

What is a rational number?

A

A number that can be written as p/q

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2
Q

Which of the following is an irrational number?

A

√3

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3
Q

The set of real numbers is the union of which two sets?

A

Rational and Irrational numbers

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4
Q

The symbol for rational numbers is __.

A

Q

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5
Q

The word ‘rational’ comes from __.

A

Ratio

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6
Q

All numbers on the number line are real numbers.

A

True

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7
Q

A repeating decimal is always a rational number.

A

True

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8
Q

Zero is neither positive nor negative.

A

True

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9
Q

A rational number can be written as a __ or a __ decimal.

A

Terminating, Repeating

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10
Q

Which of the following is NOT a real number?

A

√-1

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11
Q

Question

A

Answer 1

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12
Q

What is the origin on a number line?

A

The point labeled 0

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13
Q

Which numbers are to the right of 0 on a number line?

A

Positive numbers

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14
Q

Which property states that a + b = b + a?

A

Commutative Property

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15
Q

The sum of any two real numbers is always a __ number.

A

Real

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16
Q

A terminating decimal has an __.

A

End

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17
Q

Which of the following is a non-terminating repeating decimal?

A

0.185185185…

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18
Q

The multiplicative identity is __.

A

1

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19
Q

Which property states that (a + b) + c = a + (b + c)?

A

Associative Property

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20
Q

For each real number a

A

there exists an element -a such that a + (-a) = __.

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21
Q

The product of any two real numbers is always a __ number.

A

Real

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22
Q

Which property states that a × b = b × a?

A

Commutative Property of Multiplication

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23
Q

What is the reflexive property of equality?

A

a = a

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24
Q

If a = b and b = c

A

then a = c. This describes which property?

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25
The inequality property that states exactly one of a < b
a = b
26
Zero is neither __ nor __.
Positive
27
If a × 1 = a
then 1 is the __ identity.
28
Which property states that a(b + c) = ab + ac?
Distributive Property
29
The inverse of addition is __.
Subtraction
30
If a × a' = 1
then a' is called the __ of a.
31
What does the transitive property state?
If a > b and b > c, then a > c
32
Which property states that if a < b
then a + c < b + c?
33
What happens when both sides of an inequality are multiplied by a negative number?
The inequality sign reverses
34
In the radical expression √a
'a' is called the __.
35
The symbol √ is called the __ symbol.
Radical
36
In the expression ∛8
what is the index?
37
Which of the following represents a square root?
√25
38
The principal square root of 16 is __.
4
39
Which of the following is a cube root?
∛27
40
True or False: √16 has two possible values
4 and -4.
41
If n is not specified in a radical expression
what is the assumed index?
42
The radical form of the 5th root of 32 is __.
∜32
43
The exponential form of the 4th root of 16 is __.
16^(1/4)
44
Which of the following is NOT a radical expression?
5^2
45
If a = 36
then √a = __.
46
The square root of a negative number is __.
Not a real number
47
The index of the radical in the expression ∜81 is __.
4
48
If a = b
then b = a. This represents which property?
49
If x² = 49
then x = __.
50
Which of the following is NOT an example of a radical expression?
7^3
51
What is the nth root of a called in radical notation?
Radical
52
Which of the following represents the radical symbol?
√
53
If n is not specified in a radical
what is the default index?
54
What is the term for a number under a radical sign?
Radicand
55
What does the product rule of radicals state?
√a * √b = √(a*b)
56
The quotient rule of radicals states:
√(a/b) = √a / √b
57
Convert √9 to exponential form.
9^(1/2)
58
Convert 4^(1/3) to radical form.
∛4
59
True or False: The principal square root of 16 is only 4.
True
60
Which of the following is a valid radical expression?
∛27
61
What is the index in the radical expression ∜81?
4
62
What is the base in the expression 5^3?
5
63
What does the power rule of exponents state?
(a^m)^n = a^(m*n)
64
What is the value of 5^0?
1
65
What is the result of 3^(-2)?
1/9
66
If a^m * a^n = a^(m+n)
what is this rule called?
67
If a^m / a^n = a^(m-n)
what is this rule called?
68
If (ab)^n = a^n * b^n
what is this rule called?
69
Which set includes only positive whole numbers starting from 1?
Natural Numbers
70
Which set includes 0 along with natural numbers?
Whole Numbers
71
Which set includes all positive and negative whole numbers along with zero?
Integers
72
Which set includes numbers that can be expressed as p/q
where q ≠ 0?
73
Which of the following is an irrational number?
√2
74
The sum of a rational and an irrational number is always:
Irrational
75
True or False: The set of rational numbers is a subset of real numbers.
True
76
Which of the following represents the set of natural numbers?
N = {1,2,3,...}
77
Which of the following represents the set of integers?
Z = {0, ±1, ±2,...}
78
Which of the following represents the set of whole numbers?
W = {0,1,2,3,...}
79
Which of the following represents the set of rational numbers?
Q = {p/q | p, q ∈ Z, q ≠ 0}
80
What is the conjugate of a complex number Z = a + bi?
a - bi
81
If Z₁ = 3 + 2i and Z₂ = 1 - i
what is Z₁ + Z₂?
82
If Z₁ = 3 + 2i and Z₂ = 1 - i
what is Z₁ - Z₂?
83
What is the formula for multiplying two complex numbers Z₁ = a + bi and Z₂ = c + di?
(ac - bd) + i(ad + bc)
84
What is the formula for dividing two complex numbers Z₁ / Z₂?
(ac + bd) / (c² + d²) + i(bc - ad) / (c² + d²)

Mathematics (2 decks)

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