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
Please help me I’m so confused
Aloiza [94]

Answer:

In this situation, I would rather have hypersecretion, this means that there is an excess of adrenaline produced. Due to the fact that adrenaline triggers the body's fight-or-flight response you will be ready flee when you see the rattlesnake. If you have hyposecretion, there will be less adrenaline, meaning you may react slower and not be as prepared, possibly resulting in you getting bit.

8 0
3 years ago
Read 2 more answers
When elongated, tube-shaped cells from the lining of the intestine are treated with a certain chemical, the cells sag and become
Vlada [557]

Answer:

Microtubules

Explanation:

These filament-like structures are a major component of the cytoskeleton of the cell and help is maintain asymmetrical cell shape. They are composed of tubulin molecules arranged to form a 'hollow straw' attached to the cell membrane end to end . The contraction and lengthening of these microtubules are controlled by the addition of removal these of tubulin molecules to vary its length.

5 0
3 years ago
What is the relationship between substance abuse and the spread of STIs?
Delicious77 [7]
Substance abuse can spread STIs because when a user shares needles with an infected person, it can spread through the blood. Any high-risk behavior like this spreads STIs.
4 0
3 years ago
The blockage of cerebrospinal fluid (csf) outflow in the brain can cause accumulation of fluid, resulting in cranial enlargement
alisha [4.7K]

The correct answer is hydrocephalus.

Hydrocephalus refers to the condition in which the accumulation of fluid takes place in the ventricles (cavities) deep inside the brain. The excess fluid enhances the size of the ventricles and applies pressure on the brain. The cerebrospinal fluid usually flows via the ventricles and bathes the spinal column and the brain.

6 0
2 years ago
Eukaryotic cells in the leaf of a plant A. lack mitochondria and chloroplasts.B. lack mitochondria but have chloroplasts.C. have
olga_2 [115]
The answer is D has mitochondria and chloroplasts. In the leaf, so must have chloroplast, most eukaryotic cells have mitochondria (powerhouse of the cell)
6 0
3 years ago
Other questions:
  • In the carbon cycle, carbonate rocks would be most likely to be part of the which of earth's spheres?
    12·1 answer
  • What did Mendel's cross-pollination of pea plants prove?
    7·1 answer
  • This is when a group of animals live together and help each other, nest, find food, work, and for protection.​
    9·1 answer
  • Name four cycles that help to recycle matter in the biosphere
    15·1 answer
  • Compare diffusion and facilitated diffusion
    7·1 answer
  • Which statements accurately describe hot spots? Check all that apply.
    9·2 answers
  • Trứng có trước hay con gà có trước ?
    8·1 answer
  • The process of the formation of ATP is known as ______.
    15·2 answers
  • Which of the following statements provides the best explanation of what happens to chemicals that pollute aquifers? a. anaerobic
    9·1 answer
  • In the PNS, the neuron cell bodies are found in clusters called ________. Group of answer choices white matter ganglia columns t
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!