Algebra 2

What is the product of a complex conjugated?

The product of complex conjugates is a difference of two squares it is always a real number.

The product a complex conjugates may be written in standard form as a + bi where neither a nor b is zero.

The product of complex conjugates is a sum of two squares and is always a real number.

The product of complex conjugates is the same as the product of opposites.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. (a+bi)(a-bi) = a^2 - (bi)^2 = a^2 - b^2 i^2
    But i^2 = -1, so that makes it a^2 + b^2

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    👤
    oobleck
  2. how does this help im still confused

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  3. The answer is A: the product is the difference of 2 squares and always a real number.
    ***Do NOT let the words "Complex Number" freak you out.***
    It's still the same as any real numbers used before with just the addition of the imaginary unit of (i). When you have (i)^2 then it becomes a -1 in place of that square. So an example would be: (2+3i)(2-3i)=2(2+3i) + -3i(2+3i) with the "distributive property" of algebra/mathematics. <JUST TAKE THE 2nd PART AND PUT IT THROUGH THE 1st>
    Then do the math operation like you've always done to get: (4+6i)+(-6i-9i^2) = (4+6i)+(-6i-9(-1))
    combine like terms, simplify if possible, then write in standard form: the +6i & -6i cancel each other out, the i^2 becomes a -1 to be multiplied into the -9 to = +9 then write correctly after simplifying: 4+9=13 so 13 is the answer
    ***hope that helps***

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. english

    Which option describes a clause? the structure of a sentence a group of words containing a subject and a verb working together ******** a group of words containing an adjective and a pronoun a group of words that are similar in

  2. English

    Which of the following is a simple sentence? A. Many are called, but few are chosen B. A penny saved is a penny earned C. Fools rush in where angels fear to tread D. If at first you don’t succeed, try, try again 2. Which of the

  3. test

    A city planner is designing a new apartment complex. The complex will have several apartment buildings as well as a paved parking area for residents. In one to two sentences, describe two ways the planner can help minimize the

  4. English

    Identify the structure used in each of the sentences below. 1. The hamburger came from Hamburg, Germany, and the hot dog came from Frankfurt. simple compound complex compound-complex 2. The idea of placing meat on a bun, however,

  1. Calculus

    How is the product of a complex number and a real number represented on the coordinate plane? A)When 3 + 2i is multiplied by 3, the result is 9 + 6i. Graphically, this shows that the product is a scalar and a counterclockwise

  2. Grammar

    Label each sentence below as simple, compound, complex, or compound-complex. 1. You can enter the data, or you can interview the candidates. (compound) 2. No one knew the man, and no one asked his name. (compound) 3. After the

  3. English

    Choose the term that describes the type of sentence shown. If you are in line early, you'll be sure to get the best tickets. A.) compound-complex B.) complex C.) compound D.) simple I think it is C? John was late to dinner and I

  4. Science

    Question 12 A) Use the scenario to answer the question. A city planner is designing a new apartment complex. The complex will have several apartment buildings as well as a paved parking area for residents. In one to two sentences,

  1. Chemistry

    8-hydroxyquinoline (Q) can complex and precipitate many metals. A mixture of the aluminium and magnesium complexes weighed 1.0843g (MW=459.43; 312.61). When ignited, the mixture decomposed and left a residue of Al203 (MW 101.96)

  2. chemistry

    The solubility product for Zn(OH)2 is 3.0x10^-16. The formation constant for the hydroxo complex,Zn(OH)4^2- , is 4.6x10^17. What is the minimum concentration of OH- required to dissolve 1.6×10−2 mol of Zn(OH)2 in a liter of

  3. Chemistry

    1.) Explain the similarity between Mg(OH)2 and Zn(OH)2 in particular why would any insoluble hydroxide tend to dissolve in an acidic solution? Are they both bases? 2.) Explain the difference in particular how does Mg^+2 appear to

  4. maths

    the sum of N positive integers is 19. what is the maximum possible product of these N numbers? thx. Nice problem. Let's look at some cases 1. N=2 clearly our only logical choices are 9,10 for a product of 90 It should be obvious

View more similar questions or ask a new question.