1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Andrews [41]
3 years ago
12

Identify the values of x and y that would make the following expression represent a real number.

Biology
2 answers:
lord [1]3 years ago
7 0
I think the correct answer from the choices listed above is option C. The values of x and y that would make the expression to represent a real number would be that <span> x = 4, y = –5. Substituting and simplifying,

</span><span>(4 + 5i)(4 - 5i)
</span>16 - 20i + 20i - 25i²
16 - 25(-1)
16 +25
41
Sunny_sXe [5.5K]3 years ago
7 0

x = 4, y = -5

<h3>Further explanation</h3>

This is a problem with complex numbers.

A complex number is a number of the form \boxed{ \ z = x + yi \ } where x and y are both real  numbers.

  • x is considered the real part of the complex  number.
  • y is considered the imaginary part of the complex  number.
  • The real part of a complex number \boxed{ \ z = x + yi \ } is denoted by \boxed{ \ Re(z) \ }.
  • The imaginary part of a complex number is denoted by \boxed{ \ Im(z) \ }.
  • The modulus of a complex number \boxed{ \ z = x + yi \ } is denoted by \boxed{ \ |z| \ } and defined to  be \boxed{ \ |z| = \sqrt{x^2 + y^2} \ }
  • Remember this \boxed{ \ i^2 = (\sqrt{-1})^2 = -1 \ }

For example, \boxed{ \ z = 3 - 4i \ }

  • Re(z) = 3
  • Im(z) = -4
  • The modulus \boxed{ \ |z| = \sqrt{3^2 + (-4)^2} = 5 \ }  

Let's look at the key problem.

We must identify the values of x and y that would make the following expression represent a real number.

\boxed{ \ = (4 + 5i)(x + yi) \ }

\boxed{ \ = 4(x + yi) + 5i(x + yi) \ }

\boxed{ \ = 4x + 4yi + 5xi + 5yi^2 \ }

\boxed{ \ = 4x + 4yi + 5xi - 5y \ }

At this point, 4yi and 5xi must be of equal value and marked opposite, so that the expression represents real numbers.

\boxed{ \ 4y = - 5x \ }

Become a fraction, i.e.,

\boxed{ \ \frac{x}{y} = \frac{-4}{5} \ or \frac{x}{y} = \frac{4}{-5} \ }

From the options, the answer is C.

\boxed{ \ x = 4, y = -5 \ }

- - - - - - -

Let's check back to expression.

\boxed{ \ = (4 + 5i)(x + yi) \ }

\boxed{ \ = 4x + 4yi + 5xi - 5y \ }

x = 4 dan y = - 5 ⇒ \boxed{ \ = 4(4) + 4(-5)i + 5(4)i - 5(-5) \ }

\boxed{ \ = 16 + -20i + 20i + 25 \ }

\boxed{ \ = 16 + 25 \ }

\boxed{ \ = 16 + 25 \ }

Thus the expression represent a real number of 41.

<h3>Learn more</h3>
  1. The midpoint brainly.com/question/3269852
  2. The piecewise-defined functions brainly.com/question/9590016
  3. The composite function brainly.com/question/1691598

Keywords: identify, the values of x and y, the following expression, represent a real number, (4 + 5i)(x + yi), a complex number, real, imaginary

You might be interested in
What is the answer to this?<br><br> Brainliest to the Brainliest answer!
morpeh [17]

Answer:

C - Ammonia

Explanation:

Ammonia is a highly toxic compound that is detrimental to one’s body. This toxic compound is often, and must be transformed into urea (uric acid) before being excreted from the body.

4 0
3 years ago
Which of the statements regarding enzymes is FALSE? *
Lynna [10]

Answer:

Enzymes can only be used once

Explanation:

Enzymes are there forever

8 0
3 years ago
Which clients are showing manifestations of infection? select all that apply?
ch4aika [34]
<span>A typical questions asking someone to point out something given a selected sample would have provided enough visual data that is sufficient to make a conclusive decision from. So given a chart or a table with certain number of clients showing no signs of infection and others with infection. It's easy to pick the numbers from the chart or table. In the given question, there is no chart or table and as such, not enough data with which a conclusive and coherent answer can be arrived at.</span>
6 0
3 years ago
Which of the following actions would decrease global warming?
ludmilkaskok [199]

Explanation:

Where possible, we can switch to renewable sources of energy (such as solar and wind energy) to power our homes and buildings, thus emitting far less heat-trapping gases into the atmosphere.

8 0
2 years ago
Name the two things that power measures
Ipatiy [6.2K]
Power measures work and time

power=work/time
3 0
3 years ago
Other questions:
  • Can organisms create their own energy? Explain your answer
    6·1 answer
  • Parts of the rock in the picture are breaking down and mixing into the soil. This process is referred to as
    13·2 answers
  • Does anyone know what breed of cat this is?
    13·1 answer
  • How does Propionibacterium acnes cause acne in humans?
    10·2 answers
  • Assume that two species are coexisting in the same environment. Species A has little gene pool variation, whereas species B has
    7·1 answer
  • What is called the next step in scientific method following making a prediction
    14·2 answers
  • Why is weeding flower beds so imprortant?
    15·1 answer
  • What is the next step in the scientific method following forming a hypothesis A.stating the question B.Analyzing the data C. Con
    11·1 answer
  • Why do the rate at which enzymes catalyze their reactions decrease when cellular atp levels are high
    15·1 answer
  • How is Hydropower practical for used in business, home, or schools today?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!