Which pair of complex numbers has a real number product

Posted By Admin @ September 03, 2022

Question:

BEST ANSWER GETS A METAL!!!!

Which pair of complex numbers has a real-number product?
(1 + 3i)(6i)
(1 + 3i)(2 – 3i)
(1 + 3i)(1 – 3i)
(1 + 3i)(3i)

Answer:

we will proceed to verify each case to determine the solution

remember that

i^{2} =-1

case A) (1 + 3i)(6i)

applying distributive property

(1 + 3i)(6i)=1*6i+3i*6i \\=6i+18i^{2}\\=6i+18*(-1)\\=6i-18

-18+6i ------> is not a real number

therefore

the case A) is not a real number product

case B) (1 + 3i)(2-3i)

applying distributive property

(1 + 3i)(2-3i)=1*2+1*(-3i)+3i*(2)+3i*(-3i)\\=2-3i+6i-9i^{2}\\=2+3i-9*(-1) \\=11+3i

11+3i ------> is not a real number

therefore

the case B) is not a real number product  

case C) (1 + 3i)(1-3i)

applying difference of square

(1 + 3i)(1-3i)=(1)^{2}-(3i)^{2}\\=1-9i^{2}\\=1-9*(-1) \\=10

10 ------> is a real number

therefore

the case C) is  a real number product  

case D) (1 + 3i)(3i)

applying distributive property

(1 + 3i)(3i)=1*3i+3i*3i \\=3i+9i^{2}\\=3i+9*(-1) \\=3i-9

-9+3i ------> is not a real number

therefore

the case D) is not a real number product

the answer is

(1 + 3i)(1-3i)

     

Similar Questions

  1. Find two positive real numbers whose product is a maximum
  2. Find the product of a complex number and its conjugate
  3. Find the real and imaginary parts of the complex number
  4. 7 less than the product of 2 and a number
  5. 9 less than the product of 9 and a number.
  6. 1 less than the product of 2 and a number
  7. All real numbers at least 8 and at most 0
  8. 7 less than the product of 5 and a number
  9. All real numbers at most 9.5 or at least 5.5
  10. The product of a rational and irrational number is rational
  11. The product of 2 and the cube of a number.
  12. Which of the following pairs of numbers contain like fractions
  13. 6 more than the product of 5 and a number
  14. Which of the following pairs of numbers contains like fractions
  15. 9 less than the product of 9 and a number
  16. 6 less than the product of 3 and a number
  17. How do you write all real numbers in interval notation
  18. All real numbers at least 6 and at most 3
  19. 3 minus the product of 2 and a number x
  20. Among all pairs of numbers with a sum of 16
  21. 3 less than the product of 5 and a number
  22. Four less than the product of three and a number
  23. The product of the square of a number and 8
  24. The product of a number and 7 increased by three
  25. How are real numbers used to describe real world situations
  26. 8 less than the product of 4 and a number
  27. Give an example of a real number that is irrational
  28. 4 less than the product of 6 and a number
  29. 2.09 unit test radicals and complex numbers - part 1
  30. A all real numbers b all real numbers c yes
  31. Which number is irrational an integer and a real number
  32. How to graph all real numbers on a number line
  33. A number multiplied by another number to find a product
  34. What is the additive identity of the complex number 14+5i
  35. One minus the product of four and a number x
  36. What is the additive inverse of the complex number 9-4i
  37. How to find the absolute value of a complex number
  38. Which property of real numbers is shown below 6 0
  39. Name the property of real numbers illustrated by the equation
  40. One minus the product of four and a number x.
  41. Which number is rational an integer and a real number
  42. Express the complex number in trigonometric form. 2 - 2i
  43. Write the expression as a complex number in standard form
  44. Which of the following statements are true of a transversal
  45. How are hereditary diseases passed from one generation to another
  46. How do the global systems interact to affect ecosystems quizlet
  47. What is the effect of telomere caps on cancer cells
  48. The rate of flow of electric charge is measured in
  49. A clause that may be used as a subject complement
  50. Why is the battle of midway considered a turning point
  51. A success of the articles of confederation was that it
  52. Which of the following is not a result of globalization
  53. Select the answer that best describes what cultural competence is.
  54. Which of the following would be considered a transgenic organism
  55. Which best describes what is needed to make hardware function
  56. A war fought by the united states in the 1900s
  57. Define push factor and give some examples of push factors
  58. What is black and white and has lots of problems
  59. Who is the artist most closely associated with parisian rococo
  60. How to determine if a function is even or odd
  61. Define a constructor as indicated. sample output for below program:
  62. Give two ways the unit for acceleration can be written
  63. What do the signers of the declaration of independence pledge
  64. Which of the following are phylogenetic trees also known as
  65. Which is not an example of a risk management strategy
  66. Identify the type of each reaction in the copper cycle.
  67. Explain how to identify a starting position on a line
  68. Which of the following is an example of positive punishment
  69. How many square feet does a bag of mulch cover
  70. Which statement best describes how media can shape public policy
  71. Professor moody repeatedly put the imperius curse on harry until
  72. For which pairs of functions is and and and and
  73. At its peak a tornado is 60 m in diameter
  74. A 255 ml round bottom flask is weighed and found
  75. How to write the point slope form of an equation

I love thee to the depth and breadth and height

Answer:Let me count the ways. I love thee to the depth and breadth and height My soul can reach, when feeling out of sight For …

The declaration of independence elaborates on the enlightenment idea of

Explanation: c religious freedom and natural rights

How did the intolerable acts lead to the american revolution

Answer:Unlike previous controversial legislation, such as the Stamp Act of 1765 and the Townshend Acts of 1767, Parliament did not repeal the Coercive Acts. Hence, …

Which lists all of the x-intercepts of the graphed function

Keywords: Graph, function, interceptions, horizontal axis, cut points For this case we have a function graph and they ask us to find all the intercepts …

The main point of the epigenetic view of development is

Similar to the epigenetic view, the The neuroconstructivist view emphasizes the importance of interactions between experience and gene expression in the brain's development.This view indicates …

A weather balloon is inflated to a volume of 2.2

The density (d) of a substance is calculated by dividing the mass (m) by the given volume (v). Mathematically, d = m / vSubstituting the …

Match each creation myth feature to the correct story outline.

1 (creation from nothing) - C, the story is of God creating earth from nothing. 2 (small amount of earth expanding) - A, the story …

A type of graph suited to show change over time

Answer:Line graphExplanation:A line graph is used to represent changes over a period of time. It is better to use line graphs, when the changes are …

Which of the following is a benefit of shelterwood harvests

Answer:Option (C) Explanation:Shelterwood harvesting refers to the development of cutting down the forest that results in the formation and evolution of new seedlings of any …

At which point in the action does this story begin

The correct answer is: B.The middle. There are several narrative structures to tell a story. In this case, the narrative is non-linear, where the order …

Which statement best describes the visible color of an object

the component of light reflected by that object so the answer is b.

The space between the cornea and the iris is the

Answer:Anterior chamber.Explanation:Anterior chamber fluid filled space between the cornea inner most surface called as endothelium and iris inside the eye. Cornea is the transparent, outer, …

What were the early people of colombia very good at

They were good at trading

Which situations result in an increase in the national debt

The increase in intergovernmental debt is a situation that always result to an increase in the national debt.What is a national debt?A national debt refers …

What gametes are possible from a plant that is gg

Answer: A. gk, gKThe scientist doing a dihybrid crossing using plants with a genotype ggKk. To make the Punnet square, you need to understand how …