Show that (√7+i√3/√7-i√3 + √7-i√3/√7+i√3) is real​

Answers

Answer 1

Answer:

Step-by-step explanation:

Show That (7+i3/7-i3 + 7-i3/7+i3) Is Real
Answer 2

Step-by-step explanation:

[tex]\large\underline{\sf{Solution-}}[/tex]

Consider,

[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]

On taking LCM, we get

[tex]\rm \:  =  \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]

and

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]

So, using these Identities, we get

[tex]\rm \:  =  \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]

[tex]\rm \:  =  \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]

So, using this, we get

[tex]\rm \:  =  \: \dfrac{2(7 - 3)}{7 + 3} [/tex]

[tex]\rm \:  =  \: \dfrac{2 \times 4}{10} [/tex]

[tex]\rm \:  =  \: \dfrac{4}{5} [/tex]

Hence,

[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]


Related Questions

Can you Helppp please

Answers

To have infinite solutions both equations need to be equal

Since they subtract 5 from the right side, subtract 5 from the left side.

X is multiplied by 1/2 on the left , so multiply x by 1/2 on the right side.

1/2x -5 = 1/2x-5

Help plz !!
What are the dimensions of AB?

Answers

Answer: c.2*1

Step-by-step explanation: in the picture

You need to remember two definitions.

First, the dimensions of a matrix are the number of rows by the number of columns. If a matrix has a row and b columns, it's an a*b matrix.

Second, before computing the product of two given matrices, you need to check an important condition.

If a matrix A has i row and j columns. And a matrix B has k row and l columns we can not apply the product AB only if j = k. In other words the numbers of columns of A (j) must be equal to the number of rows of B (k).

If this condition is checked, than the new matrix will be of dimensions : ixl

In our case i = 2, j = 3, k = 3, l = 1

So the dimensions will be 2x1 so the answer is C.

Good luck

3/8 times 1/2
Help me please! I’ll give the first answer Brainiest and five stars the second one will get 4 stars ⭐️ ⭐️⭐️

Answers

Step-by-step explanation:

[tex] \frac{3}{8} \times \frac{1}{2} [/tex]

3×1= 3

---

8×2=16

thus your answer is

[tex] \frac{3}{16} [/tex]

Hope this helped you- have a good day brocya)

Answer:

[tex]\frac{3}{16}[/tex]

Step-by-step explanation:

Hey there,

[tex]\frac{3}{8} *\frac{1}{2} \\[/tex]

[tex]\frac{3*1}{8*2}[/tex]

[tex]\frac{3}{16}[/tex]

Hope this helps you.

Let me know if you have any other questions:-)

Find the value of the power. (2/3)3  ​

Answers

Answer:

8/27

Step-by-step explanation:

[tex](\frac{2}{3})^3 = \frac{2}{3} * \frac{2}{3} * \frac{2}{3} = \frac{8}{27}[/tex]

please answer the question :]

Answers

oh my god what is this, i rather die than do this im so sorry but i cant help

PLEASEE I NEED THIS ANSWER ASAP PLEASE!!

Answers

Answer:

D

Step-by-step explanation:

Find X in the triangles

Answers

Answer:

8. 14x+6+16x+4=130

30x+10=130

30x+10-10=130-10

30x=120

x=4

10. 11x+3-85=5x-10

11x+3-85-5x=5x-10-5x

6x+3-85=-10

6x+3-3-85+85=-10-3+85

6x=72

x=12

Step-by-step explanation:

5 litres into grams.​

Answers

Step-by-step explanation:

Do like this only with no. mark me as brainliest answer

Answer:

Weight in Grams of:

Water     Cooking Oil

5,000 g    4,400 g

Step-by-step explanation:

Hope this helps

Use a common denominator to find equivalent fractions for 1/3 and 4/5

Answers

Common denominator is 15

1/3 = 3/15
4/5 = 12/15

O Domingos tinha certa quantia em dinheiro, foi ao centro comercial e gastou 1/3 da quantia na compra de uma revista, gastou 1/4 da quantia na compra de um CD e ainda ficou com 25 mil kzs. Qual era a quantia que Domingos possuía?

Answers

Answer:

English

Step-by-step explanation:

Below is a recipe for chocolate chip cookies. The recipe makes 27 cookies. How many teaspoons of vanilla extract do you need to make 24 cookies? Round to the nearest hundredth if needed.

Answers

Answer: 1.78 teaspoons

Step-by-step explanation:

The recipe says: 27 cookies/2 teaspoons Vanilla extract. Let's abbreviation this conversion factor as (27/2)C/V, where C is cookie and V is 1 teaspoon vanilla extract. We have both 13.5C/V and 1V/13.5C as conversion factors. 13.5 cookies is equivalent to 1 teaspoon vanilla, or 1 teaspoon vanilla is equivalent to 13.5 cookies. We can multiply ofr divide either of these factors, since they are both equivalent to 1, and you can mukltiply or divide anything by 1 without changing it's accuracy. The atual numbers will change, but the units will also change, making it a valid result.

We want 24 cookies. Use one of the conversion factors to find the teaspoons vanilla extract required:

1) We can divide by (27C/2V)

24C/((27C/2V) = 1.78 teaspoons

or

2) we can multiply by (1V/13.5C)

24C*(1V/13.5C) = 1.78 teaspoons

Using suitable property, find the value of 689 × 147- 689 × 47
and mention the property used.

Answers

Answer:

Step-by-step explanation:

689×147-689×47

=689(147-47)

=689(100)

=689×100

=68900

sas, sss, aas, or not enough information

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Two Angles and the side between them are equal to corresponding Angles and side of another triangle ( one of the Angles are equal because of vertical opposite angle pair ), so the required congruency criteria to prove them equal is :

ASA

Answer:

ASA

Step-by-step explanation:

Help me

Number questions

Answers

Step-by-step explanation:

a) Four thousand five hundred thirty-six.

b) arrange in descending order

3456.

c) since we have to make odd number therefore once digit will be odd , 3 ( or 5 too )

so, the number is 6543.

hope this answer helps you dear!

Find the equation of the linear function represented by the table below in slope-
intercept form.

Answers

Answer:

Hey there, first let's find the slope.

M=y2-y1/x2-x1.

M=7-3/2-1 which is 4/1.

So your slope is 4

So now we have y=4x+b.

Now we need our Y-intercept (B). which is -1

So your answer is Y=4x-1

Write the equation of the line shown in the graph to the right
Hint: Think about slope and y-intercept.

Answers

Answer:

y=2x-6

Step-by-step explanation:

The intercept is -6 so -6 and you take two points on the line e. g. (3,0) and (2,-2) You would do -2-0 to get -2 and 2-3 to get -1. -2 divided by -1 equals 2. The slope is two.

A breakfast stall at a market stays open for 4 hours 30 minutes every morning. If it opens at 06:45 every morning, what time did he reach​

Answers

Answer:

uhj hdctui nomar binary 34.89

Explain how you can mentally determine that 35000 divided by 70 is 500

Answers

Firstly, 35 = 7 x 5

Thus, ignoring the zeroes, we can see that 35000 / 7 would be 5000. Then, divide it by 10 to get 500.

pls mark me as brainliest!

Find the unknown sizes of angles in the following figures (with step-by-step explanation please):​

Answers

Answer:

O= 87 degrees

Step-by-step explanation:

Because they are opposites

Answer:

x angle is 29

then 2x angle is 58 and y angle is complementary so then y also is 58

express 5^20 as a power of 25

Answers

5^20 can be written as (5^2)^10=25^10

The expression of 5^20 as a power of 25 can be written as 25^10.

What are exponents?

The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.

We need to express 5^20 as a power of 25

If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" means this statement might change from text to text slightly.

Thus, 5^20 can be written as ;

(5^2)^10 = 25^10

Therefore, the expression of 5^20 as a power of 25 can be written as 25^10.

Learn more about exponentiation here:

https://brainly.com/question/26938318

#SPJ2

. Excel Secondary School wants to send its students for an educational trip and has found an organisation that is willing to sponsor up to an amount of $2 500 for the trip. Given that the cost of sending a student for the trip is $12, what is the maximum number of students the school can send for the trip if it relies only on the sponsorship?​

Answers

Answer:

208 students I think that's the answer

! ! ! Angles ! ! !
(worth ten points)
Which is the best explanation of why triangles ABC and ACD are similar?
A.) Both triangles are right triangles.
B.) Both triangles contain angles A and C.
C.) Both triangles a right angle and angle A.
D.) Both triangles contain a right angle and angle C.

Answers

Answer:

the answer is a :)

Step-by-step explanation:

Identify the domain and range of the following relation. {(7,-2), (7,4), (7,6), (7,-4), (7,1)

Answers

Answer:

look at explanation

Step-by-step explanation:

domain= all the 7s

range: -2, 4, 6, -4, 1

What were two impacts of the first great depression?

help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

1: unemployment (more homeless people)

2: House prices rose down drastically by 70%.

(My sources: TheBalance.com)

I really need help please someone

Answers

Answer:

B) She puts the flag in the window after the men have taken it down.

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

She puts the flag in the window after the men have taken it down.

When President Obama stated, "Transparency and the rule of law will be the touchstones of this presidency," he meant that

Answers

Answer:

that what

Step-by-step explanation:

Shylan's vegetable garden is florishing. She has
20 plants in her garden which are broken into
equal rows. 1/5 of the rows are cucumbers and
40% of the rows are squash. 1/2 of the
remaining rows are tomatoes. How many
pepper plants does she have?

Answers

Answer: 90millionhajk

Step-by-step explanation:

how many times dose the average person do math a day?

Answers

A little depends on the person

Dylan invested some money in his bank.
He agreed a simple interest rate of 3% per annum for a period of 2 years.
At the end of the 2-year period the value of his investment increased by £72.
Work out the value of Dylan's initial investment.

Answers

two years at 3% = .03*2 = .06

so

.06 times original deposit = 72

so 72/.06

which is

1200

Given that f ( x ) = 3 x − 7 and g ( x ) = 3 x + 9 , evaluate f ( g ( 2 ) )

Answers

Answer:

38

Step-by-step explanation:

f ( x ) = 3 x − 7

g ( x ) = 3 x + 9

f(g(2))

First find g(2)

g(2) = 3(2)+9 = 6+9 = 15

Then find f(15)

f(15) = 3*15 -7 = 45 -7 =38

Other Questions
Fat is stored under the skin of humans and many animals. Fat helps keep people and animals warm. It also helps protect areas around eyeballs and other body parts. In plants, most of the fat is stored in the seeds. The fat provides food to the seed when it first begins to grow.Is it possible to have too much fat? Of course! Doctors say that people should be careful about how much fat they eat. Most foods have a little fat, but a person can get sick if he or she eats a large amount of food with too much fat.Which sentence shows an idea that would be important to include in a summary of this passage? A. Fats called oils can be used to fry food. B. Fats are found in animals and plants. C. Butter is made mostly of animal fat. D. Margarine is made mostly from plant fat. Kiran has 27 nickels and quarters in his pocket, worth a total of $2.75.a. Write a system of equations to represent the relationships between thenumber of nickels n, the number of dimes d, and the dollar amount inthis situation. in a sale, a clothes shop reduces its price by 45%.a shirt usually costs $27how much is it on sale? As part of studying civics, it is important for U.S. citizens to know?A. How mayors are electedB. how state income taxes are collectedC. how the economy worksD.how refugees can enter the countryHURRYYYY PLZ HELP, WILL GIVE BRAINLIESTWhich scenario best describes natural selection? a species of flower develops a gene that results in a more attractive nectar causing more pollinators to be attracted wheat plants are selected for their ability to produce the most wheat germ a bacteria exposed to radiation acquires a mutation a hurricane occurs and kills 70% of the members of a rodent species If a FRAMESHIFT mutation causes a stop codon to be inserted into the DNA sequence which type of fossils are used to identify specific time periods? what is the height if a painting is 1 centimeters and represents as 9 inches help me guys I don't get this !!! NEED HELP!!!! 15 POINTS!!!!Which BEST explains why it is important to warm up before strenuous exercise?A. It is very hard on the joints when exercise begins without warm up.B. It strains the muscles if blood and oxygen levels are not already activated.C. Warm-ups limit the oxygen supply, prepping the body for the rush during exercise.D. An exercise session should not include more than 30 minutes of aerobic activity. Find the value of x so that L||M If the second quantity in a rate is not 1, how do you find the unit rate? Does a strict liability case necessarily include an ultrahazardous activity?O A. Yes, because ultrahazardous activities are strict liability claims.O B. Yes, because strict liability is based on fault.O C. No, because it may include a defective product.D. No, because an ultrahazardous activity is a negligence action. The probability that a red block is selected from a bucket is3/8, and the probability that a blue block is selected is 2/8.What is the probability that a red block or a blue block isselected?a) 1b) 1/2c) 5/8d) 6/8 100 points will mark BRAINLYEST Define the type of muscle contraction that you experience most throughout your day and the one that you experience most when working out. Give examples to support your answer. A rectangular cake pan has a volume of 234 cubic inches. If the length of the pan is 9 inches and the width is 13 inches, what is the height of the pan? Part AHow does the author develop the central idea that people have varying opinions about how valuable a product is?A. The author discusses how systems for collecting taxes vary according to where people live.B. The author explains that the consumer's willingness to pay a certain price for a given item affects how the retailer sets the price.C. The author says that items such as shoes, bottled water, and garden hoses differ in price from place to place.D. The author explains that value-added tax is collected from manufacturers, retailers, and consumers.Part BWhich evidence from the text best supports the answer in Part A?A. "Once youve found all the parts you need, you could end up spending between $65 and $120 for your new garden hose!"B. "One of Germany's fiscal policies is to collect taxes in many stages during the production of items."C. "We al Need help ASAP ?!!!50 points A 125 mililiter solution of fabric dye contains 5 ml of hydrogen peroxide what percent concentration of hydrogen peroxide?