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

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?

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Answer:

English

Step-by-step explanation:

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

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Answer:

that what

Step-by-step explanation:

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

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

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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

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

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

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

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

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

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:

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

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!

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!

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​

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Answer:

uhj hdctui nomar binary 34.89

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

Shylan's vegetable garden is florishing. She has
20 plants in her garden which are broken into
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40% of the rows are squash. 1/2 of the
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Answer: 90millionhajk

Step-by-step explanation:

I really need help please someone

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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.

! ! ! 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:

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:

please answer the question :]

Answers

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

. 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

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

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:-)

PLEASEE I NEED THIS ANSWER ASAP PLEASE!!

Answers

Answer:

D

Step-by-step explanation:

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]

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)

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

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

Answers

A little depends on the person

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.

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