Mathematics High School

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

Solve for b. Express your answer as an integer or integers or in simplest radical form. -165= -3-6b^3
Fastest and correct wins brainliest

Answers

I wanna help you but I don’t understand sorry

Cleo and jandi are having a hollowed party. They have 3 1/2 pounds of candy to divide into 14 goodie bags. How much candy will be in each bag?

Answers

Answer: 1/4 pound(s) of candy in each bag

Step-by-step explanation:

Answer:

1/4 pound(s) of candy

Step-by-step explanation:

brainliest pls


The difference of half
of a number and three
is equivalent to
negative
five.

Answers

3/2=3-5

Step-by-step explanation:

jdjdnsnsnsmanzna

G.
G
7 cm
8 cm

-
Find volume

Answers

Step-by-step explanation:

The volume = [tex](\frac{22}{7} )(7^{2} )(8)[/tex]

= 1232

please give me a brainliest answer

1232 should be your answer

c. Point B (-3, -4) is also on the circle. Verify algebraically whether triangle OAB is a
right-angle triangle.

Answers

Answer:

89

Step-by-step explanation:

don't use this awnser its wrong

Wolfman and Dracula we’re having a contest to see who can scare people the most for every three people Dracula scare Wolfman scared seven if Wolfman scared 24 more people how many people were scared and all

Answers

so um i to get a new phone with him to help me with my work schedule and then i i to get my money on my way back from work so i’ll give him my bath now i and i and my mom works at the house for me a few days and i to see if he wants me a friend and 728

Solve 7!

(Need help with this in Math!)

Answers

The answer is 5040.

7! means 7x6x5x4x3x2x1

7x6x5x4x3x2x1
42 x 20 x 6
42 x 120
5040

last 2 guyss !!!! tysm

Answers

First one is a rotation 90° clockwise

Second one is B. 134°

Answer:

A 90° clockwise

B 134°

It is 12:49 what time it will be 30 minutes from now

Answers

Answer:

01:19 PM

Step-by-step explanation:

if its 12:49 then in 30 minutes it'll be 1:19pm

because

in 11 minutes I'll be 1pm and then 30-11= 19

so

1pm + 19 mins = 1:19pm

Hope this helped you- have a good day bro cya)

Answer:

1:19 pm

Hope you have an amazing day!

Find the slope of (2 , -7 ) and ( -1 , 6 )


A. 4

B. -6

C. -1/6

D. 6

Answers

Answer:

-13/3

Step-by-step explanation:

y2 - y1 / x2 - x1

6 - (-7) / -1 - 2

13 / -3

= -13/3

Hello !

Answer:

[tex] \boxed{\sf None \: of \: the \: options \text{:} \: \: m =- \dfrac{13}{3}} [/tex]

Step-by-step explanation:

The slope m of a line passing through two points can be calculated using the following formula:

[tex] \sf m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]

[tex] \\ [/tex]

Let (x₁ , y₁) = (2 , -7)

Let (x₂ , y₂) = (-1 , 6)

Substitute these values into our formula:

[tex] \sf m =\dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{6 - (-7) }{-1 - 2 } = \dfrac{13}{-3}\\ \\ \implies \boxed{\sf m = -\dfrac{13}{3}} [/tex]

Have a nice day ;)

Given the graph of f'(x) shown below, find the intervals on which the function f(x) is increasing.
See the graph attached below.

Isn't the answer supposed to be (-infinity, -2) U (1, infinity) ?

Answers

Answer:

intervals (-3,-1) and (0,+infinity)

Step-by-step explanation:

if f'(x)>0 then f is increasing

May I please receive help?

Answers

Well I’m not sure if I’m right:
This is my answer:
1

determine the H.C.F of 12,48,60​

Answers

Answer:

HCF(12, 48, 60) = 12

Step-by-step explanation:

HCF of 12, 48, 60 is 12 since 12 is largest number which exactly divides all the numbers

Highest common factor (HCF) of 12, 48, 60 is 12.

Hope this helped you- have a good day bro cya)

13. Does are turned using a special tool called a/ an

I think it’s C. die stock

Brainliest for a correct answer!!!

Answers

Answer:

You have the correct answer selected, (C.) Die stock. I hope this helps you! Good luck! : )

someone help it’s about gradients etc check photo please!! (The coordinates of K and L are (-8, -5)

Answers

Answer:

[tex]i) \frac{2}{3} [/tex]

Step-by-step explanation:

[tex] = \frac{y {}^{1} - y {}^{2} }{x {}^{1} - x {}^{ {}^{2} } } [/tex]

[tex] = \frac{ - 5 - ( - 1)}{ - 8 - ( - 2) } [/tex]

[tex] = \frac{ - 4}{ - 6} [/tex]

[tex] = \frac{2}{3} [/tex]

Josiah skateboards from his house to school 3 miles away. It takes him 36 minutes.

How many minutes will it take Josiah to skateboard to his friend Sebastian’s house, which is 2 1/2

miles from school, if he travels at the same rate that he did from his house to school?


In the box below, type the number that goes in the blank.

Answers

Using the speed - distance relationship, the number of minutes it will take Josiah to cover a distance of 2.5 miles is 30 minutes.

Calculating Josiah's speed :

Speed = (distance ÷ time)

Speed = (3 ÷ 36) = 0.08333 miles per minute.

Time taken to cover a distance of 2.5 miles :

Time taken = (Distance ÷ Speed)

Time taken = (2.5 ÷ 0.08333) = 30 minutes

Therefore, it will take 30 minutes for Josiah to cover a distance of 2.5 Miles

Learn more : https://brainly.com/question/18112348

3. Which phrase best describes the function of the ATP molecule?

1. Carries energy

2. Destroy energy

3. absorbs energy

4. none of the above

Answers

Answer:

1.) Carries energy

Step-by-step explanation:

A good summary of an ATP molecule is a molecule that transfers energy between cells... meaning it carries energy from cell to cell. Furthermore, energy cannot be destroyed, and cannot be absorbed, only changed and transformed. This leaves us with two options, (1. Carries energy, and 4. None of the above). Since we already have a basic understanding of what an ATP molecule does, we can confidently determine that the correct answer is that an ATP molecule can best be described as carrying energy.

The temperature at 6pm is
54℉. The temperature at 10pm
is 42℉. How many degrees did
the temperature fall?

Answers

Answer:

12

Step-by-step explanation:

Answer:

12°F??¿??¿????¿??!??????????

Find the domain:

(2x^2-2)/ x

Answers

Answer:

.........................

Answer:

Answer attached in the image

Ashley went to a store and bought 3 items. Each item cost $21. How much did she spend

Answers

Answer:

$63

Step-by-step explanation:

what is the first natural number
A.0 B.1. C.-1​

Answers

Answer:

1

Step-by-step explanation:

1 is the first natural number because 0 is not a natural number.

All natural numbers are numbers from 1 onward.

Ex. 1.2.3.4.5.6...

Can somebody help me with this?

Answers

Answer:

wrong

Step-by-step explanation:

(2(x + 13)) /3

the expression says x = 5, so let's check:

(2(5 + 13)) /3

36/3 = 5...FAKE

6.) Danasia has two summer jobs. During the week she works in the grocery store and on the
weekend she works at a nursery. She gets paid $15 per hour to work at the grocery store and
$18 per hour to work at the nursery. The one week she made $630. Write an equation to
model the situation.

Answers

Answer: 630 = 15x + 18y

Step-by-step explanation:

Solve for t:
t + 7 = 21

A: t= 28
B: t= 14
C: t= -28
D: t= -14

Answers

t + 7 = 21

---Subtract 7 from both sides

t + 7 - 7 = 21 - 7

t = 14

Hope this helps!! :)

Answer:

B) t = 14

Step-by-step explanation:

(Inscribed Angles)
Find m∠N.

Answers

Answer:

x=9 y=3

Step-by-step explanation:

because 5x+9=6x and 6y-1=3y+8

x=9 y=3

branlist please

<1 and <2 are complementary angles. m<1=2x+34, and m<2=2x+8. find the measure of each angle

Answers

Step-by-step explanation:

2x+34=2x+8=90°

4x+42=90°

-42. -42

4x=. 48

÷4. ÷ 4

x= 12 ( divide both sides by 4)

( you need to substitute x)

2(12)+34

measure of angle 1 is equal to 58

2(12)+8

measure of angle 2 is equal to 32

factor the expression using the gcf 2t-10​

Answers

The GCF of 10 and 2 is 2.
So, 2(t-5).

what is the slope of a line parallel to the line whose equation is 2x + y = 3?

Answers

Step-by-step explanation:

Here is the answer to the question

Answer:

-2/1

Step-by-step explanation:

Rewrite equation in point-slope form

y=-2x+3

in y=mx+b, m= the slope

The slope of the line is -2/1

Any lines parallel to this line will have the same slope

Which graph best represents the solution set of y > 5/3x + 2?

Answers

Answer:

[tex]y > \frac{5}{3} x + 2[/tex]

The choice A.

I hope I helped you^_^

Line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A prime B prime. What is the length of A prime B prime? (5 points)

a
1 unit

b
2 units

c
3 units

d
5 units

Answers

Answer:

5 units

Step-by-step explanation:

2+3=5

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