Real And Complex Numbers Flashcards
What is a rational number?
A number that can be written as p/q
Which of the following is an irrational number?
√3
The set of real numbers is the union of which two sets?
Rational and Irrational numbers
The symbol for rational numbers is __.
Q
The word ‘rational’ comes from __.
Ratio
All numbers on the number line are real numbers.
True
A repeating decimal is always a rational number.
True
Zero is neither positive nor negative.
True
A rational number can be written as a __ or a __ decimal.
Terminating, Repeating
Which of the following is NOT a real number?
√-1
Question
Answer 1
What is the origin on a number line?
The point labeled 0
Which numbers are to the right of 0 on a number line?
Positive numbers
Which property states that a + b = b + a?
Commutative Property
The sum of any two real numbers is always a __ number.
Real
A terminating decimal has an __.
End
Which of the following is a non-terminating repeating decimal?
0.185185185…
The multiplicative identity is __.
1
Which property states that (a + b) + c = a + (b + c)?
Associative Property
For each real number a
there exists an element -a such that a + (-a) = __.
The product of any two real numbers is always a __ number.
Real
Which property states that a × b = b × a?
Commutative Property of Multiplication
What is the reflexive property of equality?
a = a
If a = b and b = c
then a = c. This describes which property?
The inequality property that states exactly one of a < b
a = b
Zero is neither __ nor __.
Positive
If a × 1 = a
then 1 is the __ identity.
Which property states that a(b + c) = ab + ac?
Distributive Property
The inverse of addition is __.
Subtraction
If a × a’ = 1
then a’ is called the __ of a.
What does the transitive property state?
If a > b and b > c, then a > c
Which property states that if a < b
then a + c < b + c?
What happens when both sides of an inequality are multiplied by a negative number?
The inequality sign reverses
In the radical expression √a
‘a’ is called the __.
The symbol √ is called the __ symbol.
Radical
In the expression ∛8
what is the index?
Which of the following represents a square root?
√25
The principal square root of 16 is __.
4
Which of the following is a cube root?
∛27
True or False: √16 has two possible values
4 and -4.
If n is not specified in a radical expression
what is the assumed index?
The radical form of the 5th root of 32 is __.
∜32
The exponential form of the 4th root of 16 is __.
16^(1/4)
Which of the following is NOT a radical expression?
5^2
If a = 36
then √a = __.
The square root of a negative number is __.
Not a real number
The index of the radical in the expression ∜81 is __.
4
If a = b
then b = a. This represents which property?
If x² = 49
then x = __.
Which of the following is NOT an example of a radical expression?
7^3
What is the nth root of a called in radical notation?
Radical
Which of the following represents the radical symbol?
√
If n is not specified in a radical
what is the default index?
What is the term for a number under a radical sign?
Radicand
What does the product rule of radicals state?
√a * √b = √(a*b)
The quotient rule of radicals states:
√(a/b) = √a / √b
Convert √9 to exponential form.
9^(1/2)
Convert 4^(1/3) to radical form.
∛4
True or False: The principal square root of 16 is only 4.
True
Which of the following is a valid radical expression?
∛27
What is the index in the radical expression ∜81?
4
What is the base in the expression 5^3?
5
What does the power rule of exponents state?
(a^m)^n = a^(m*n)
What is the value of 5^0?
1
What is the result of 3^(-2)?
1/9
If a^m * a^n = a^(m+n)
what is this rule called?
If a^m / a^n = a^(m-n)
what is this rule called?
If (ab)^n = a^n * b^n
what is this rule called?
Which set includes only positive whole numbers starting from 1?
Natural Numbers
Which set includes 0 along with natural numbers?
Whole Numbers
Which set includes all positive and negative whole numbers along with zero?
Integers
Which set includes numbers that can be expressed as p/q
where q ≠ 0?
Which of the following is an irrational number?
√2
The sum of a rational and an irrational number is always:
Irrational
True or False: The set of rational numbers is a subset of real numbers.
True
Which of the following represents the set of natural numbers?
N = {1,2,3,…}
Which of the following represents the set of integers?
Z = {0, ±1, ±2,…}
Which of the following represents the set of whole numbers?
W = {0,1,2,3,…}
Which of the following represents the set of rational numbers?
Q = {p/q | p, q ∈ Z, q ≠ 0}
What is the conjugate of a complex number Z = a + bi?
a - bi
If Z₁ = 3 + 2i and Z₂ = 1 - i
what is Z₁ + Z₂?
If Z₁ = 3 + 2i and Z₂ = 1 - i
what is Z₁ - Z₂?
What is the formula for multiplying two complex numbers Z₁ = a + bi and Z₂ = c + di?
(ac - bd) + i(ad + bc)
What is the formula for dividing two complex numbers Z₁ / Z₂?
(ac + bd) / (c² + d²) + i(bc - ad) / (c² + d²)
