The product of any nonzero real number and i is called an ___________ number.

Q: Which numbers satisfy |a| = a? Which satisfy |a|=−a? What about |−a| = a?

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Q: Identify the following statement as either true or false. A number can be both rational and…

A: we have to identify the following statement is true or false

Q: et of three positive integers a, b, and c that satisfy the equation a² + b? = c² is called a(an)_…

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Q: State all real-number values of x which will make this statement true:    x  + 4 > 5 – (1 – x)

A: The given inequality is  x + 4 > 5 – (1 – x)

Q: Let a and b be nonzero real numbers and m and n be integers. Which of the following is not a law of…

A: The exponent rules are used to simplify exponential expressions . We often use exponent rules to…

Q: If a and b are integers, then a/b is always a rational number. True False

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Q: Let n be a real number and let e be a positive real number. Determine whether there exists a real…

A: see the attachments

Q: need help solving this

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Q: Give an example of each of the following: (a) A natural number (b) An integer that is not a natural…

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Q: Which of the following is not a real number? (1) (6 + 2i)(6 – 2i) (2) (–2i)12 (3) (3 + 4i)(-4i) (4)…

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Q: Give an example of each of the following:(d) An irrational number

A: To Give an example of An irrational number.

Q: Prove that if a, b e R, then (a) -(a+b) = (-a) + (-b), (b) (-a)·(-b) = a · b,

A: (a) Proof of the fact -(a+b)=(-a)+(-b): Since -1 is additive inverse of 1, hence  −1+1=0   (zero in…

Q: The cube root of any negative real number is negative.a. Given any negative real number s, the cube…

A: It is given that the cube root of any negative real number is negative.

Q: Which of the following is a binary operation on the set of positive real numbers? a. a*b = √a + √a+…

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Q: all real numbers a

A: The function is given as fx=9-xx-6 . The given function is rational function and to determine the…

Q: state the property of equality or the property of real numbers that justifies each of the…

A: Given 3(x+4)=3(x)+3(4)…(1) We need to state the property of the real number that justifies the above…

Q: Every real number is either a/an number. number or alan.

A: Consider the statement: Every real number is either a/an                        number ora/an…

Q: Let x be a real number. For what value of x, the statement if x2 < 0, then a <0 is FALSE? O x=-1.5 O…

A: From given statement

Q: Find, if possible, the following: a) Any number a for which "a < a" is true. b) Any numbers a and b…

A: (a)  given :  for any number 'a'  for  which ''a&lt;a'' is true is not…

Q: hich of the following statements is NOT true on operations on real numbers?  a. A real number…

A: Which of the following statements is NOT true on operations on real numbers?  a. A real number…

Q: find all the root of ( aº – 1=0)? 9.

A: We know that De Moivre’s formula (cos x + i sin x)^n = cos(nx) + i sin(nx)

Q: (a) Suppose x is an irrational number. Show that there is an integer n such that |x – n| < 1/2. (b)…

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Q: state the property of equality or the property of real numbers that justifies each of the…

A: Given a equality, 3(98)+3(2)=3(98+2) We need to state the property of the equality.

Q: let a and b be integers. Show: if a * b is odd, then a is odd and b is odd

A: A number is even, if it is divisible by 2. A number is odd, if it is not divisible by 2. The odd…

Q: State Archimedean property of real numbers. Hence show that for each real number ɛ> 0, there exists…

A: We write the statement of Archimedean Property of real numbers. And we proof the second part of the…

Q: state the property of equality or the property of real numbers that justifies each of the…

A: Given that : The statement , [(17)(4)](25) = (17)[(4)(25)]

Q: state the property of equality or the property of real numbers that justifies each of the…

A: According to the inverse property of multiplication: ab×ba=1 i.e. the product of a fraction with its…

Q: Every nonzero real number has a reciprocal. 12. For all nonzero 11. All nonzero real real numbers r,…

A: 11)   All nonzero real numbers have reciprocal.

Q: Question 2 * Which of the following is a true statement? A. All real numbers are rational numbers.…

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Q: If a and b are two real numbers and a <b then there is a rational number r such that a <r<b.

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Q: _1. Which of the following statements is NOT TRUE? A. Every rational number is a real number. B.…

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Q: Find non-zero real number values of a, b, c, and d such that the sum (a + bi) + (c + di) is... -a…

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Q: 1. For every real number a and b, a binary operation & is defined as: a & b 2a - 3b. a. What is the…

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: Let a and b be two positive real numbers. Let p > 1 and q> 1 be such that + = 1 (q is called the…

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Q: What two nonnegative real numbers with a sum of 46 have the largest possible product? The numbers…

A: The objective is to determine what two non-negative real numbers with the sum of 46 have the largest…

Q: (1) For all real numbers a and b, if a is a rational number and b is an irrational number, then a −…

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Q: the base of a number system can be numbers other than positive integers (such as b = -5). Recall…

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Q: Which of these, when simplified, represents an irrational number? (0.83) because the product of two…

A: As we know,                       An irrational number is a type of real number which cannot be…

Q: {x|x is a natural number and 20<x<24}

A: x | x is a natural number and 20&lt;x&lt;24

Q: True/False: if a, b are irrational numbers, then a+b is an irrational number. True False

A: A Rational Number is a type of real numbers, which is in the form of pq where q is not equal to…

Q: 1. Determine whether or not the following numbers are natural numbers, integers, or rational…

A: Since we have multiple question our guideline is solve first  question kindly repost other question…

Q: The cube root of any negative real number is negative a.) Given any negative real number s , the…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: With addition as given of (complex numbers) prove the following statement:-   The additive inverse…

A: Let C be the set of all ordered pairs ( a , b ) where a and b are real numbers Addition is defined…

Q: Any non-zero integer divides 0. O True O False

A: True or false Number system

Q: Expressing each of these numbers in the form. A+bi ie5πi/3

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Q: (a) Prove that the real number V3 is an irrational number. That is, prove that If r is a positive…

A: Rational number: A number is known as rational number if it can be expressed as the ratio of two…

Q: Describe the structure of the real number by writing a statement that summarizes when a real number…

A: describe the structure of the real number by writing a statement that summarizes (i) when a real…

Q: 24. The reciprocal of any irrational number is irrational. (The reciprocal of a nonzero real number…

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Q: 6. Let a be a real number.

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Q: Fill in the blank so that the resulting statement is true. The statement 3+3=6 serves as a/an The…

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.