Mathematics High School

If (x+iy)³ = y+vi then show that (y/x + v/y) = 4(x²-y²)​

Answers

Answer 1

Answer:

Step-by-step explanation:

If (x+iy) = Y+vi Then Show That (y/x + V/y) = 4(x-y)
Answer 2

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

Given that,

[tex]\rm \longmapsto\: {(x + iy)}^{3} = y + iv[/tex]

[tex]\rm \longmapsto\: {x}^{3} + 3 {x}^{2}(iy) + 3x {(iy)}^{2} + {(iy)}^{3} = y + iv[/tex]

[tex]\rm \longmapsto\: {x}^{3} + 3 {x}^{2}yi + 3x {i}^{2} {y}^{2} + {i}^{3} {y}^{3} = y + iv[/tex]

We know,

[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1 \: \: \: and \: \: \: {i}^{3} = - i }}} \\ [/tex]

So, using this, we get

[tex]\rm :\longmapsto\: {x}^{3} + 3 {x}^{2}yi - 3x{y}^{2} - i{y}^{3} = y + iv[/tex]

[tex]\rm \longmapsto\: ({x}^{3} - 3x {y}^{2}) + i(3{x}^{2}y- {y}^{3})= y + iv[/tex]

On comparing real and Imaginary parts, we get

[tex]\rm \longmapsto\:y = {x}^{3} - 3 {xy}^{2} [/tex]

and

[tex]\rm \longmapsto\:v = {3x}^{2}y - {y}^{3} [/tex]

Now, Consider

[tex]\rm \longmapsto\:\dfrac{y}{x} + \dfrac{v}{y} [/tex]

[tex]\rm \:  =  \: \dfrac{ {x}^{3} - {3xy}^{2}}{x} + \dfrac{ {3yx}^{2} - {y}^{3} }{y} [/tex]

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

[tex]\rm \:  =  \: {x}^{2} - {3y}^{2} + {3x}^{2} - {y}^{2} [/tex]

[tex]\rm \:  =  \: 4{x}^{2} - {4y}^{2}[/tex]

[tex]\rm \:  =  \: 4({x}^{2} - {y}^{2})[/tex]

Hence, Proved

Related Questions

Question 1
Tim is a car salesman and earns a 5% of the price of the cars he
sells: Last month he sold 8 cars for a total of $152,558.75.
Estimate the amount Tim earned last month.

Answers

Answer:

152558.75*5%=7627.9

Step-by-step explanation:

5^-1 = blank * 5^4 find the missing factor

Answers

Answer:

1/3125 or, 5^-5

Step-by-step explanation:

5^-1 = blank * 5^4

1/5/625= blank   or,     5^-1/5^4=blank

blank=1/3125               5^-5=blank

so I'm not sure how to draw a square with the area of 3 units

Answers

The area of a square is width x height where both the width and height is the same length because a square has the same lengths on all four sides.

So we can say “3 = L x L” where L is any side length of the square

L times L is just simplified to L squared: “3 = L^2”

We can take the square root of both sides to get rid of the L squared. We are left with “the square root of 3 equals L”.
Sqrt(3) = L

And on a calculator the square root of 3 is 1.73205080757.

1.73205080757 = L.

The square is 4 lines in a box each with the length of 1.73205080757 units.

Find the equation for the line that passes through the points (1, 1) And (3, 5)

Answers

Answer:

y = 2x - 1

Step-by-step explanation:

Slope = (5-1) / (3-1) = 4/2 = 2

y-intercept = 1 - (2)(1) = - 1

y = 2x - 1

rewrite the equation in standard form y = - 3/4x - 6

Answers

Answer:

3x + 4y = - 24

Step-by-step explanation:

Brainliest?

Write the Prime Factorization of the following Numbers:
(a) 10




(b) 37




(c)25

Answers

(a) 10 = 2x5

(b) 37= 1x37
(c) 25=5x5

Chase bought 5 chicken wings for $9.50. If Chase spent $26.60, how many chicken wings did he buy?

Please help me find the answer for this ( I think the answer is 14? I don't know for sure) thank you so much if you help me!

Answers

Find the price of 1 wing:

9.50 / 5 = 1.90 per wing

Divide total spent by price per wing:

26.60 / 1.90 = 14

Answer: 14

Answer:

14

Step-by-step explanation:

$9.50 / 5 = $1.90

$26.60 / $1.90 = 14


Any answers for this?

Answers

Answer:

D(t) = 2,280 - 60t

for D(15) compare the eqns and substitute the value of t.

D(15) = 2,280 - 60(15)

D(15) = 1,380 miles.

In the context of the qn, the Chang family travels 1,380 miles in 15 hours.

Kristal was writing 5,060 in scientific notation. She said that it was 5.6 x 10^3 do you agree or disagree

Answers

Answer:

I disagree

Step-by-step explanation:

It is 5.06 x 10^3

what is 843.5 x 10 with a exponent of 2

Answers

Answer:

84,350

Step-by-step explanation:

843.5 x 10^2 = answer

Answer:

84350

Step-by-step explanation:

find the GCF using factor trees 10, 54 show your work

Answers

Hiiii hows ur day going!

Without using a calulator, find A and B, A^B - B^A = 1.

Answers

Answer:

A = 1

B = 0

Step-by-step explanation:

Find the result when 68 is decreased by 50%.

Answers

Answer:

34

Explanation:

When 68 is decreased by 50%, that would mean that it is decreasing by half of that number. Half of that number would be 34 and that would be your answer.

This week a pack of tomato plants cost $25 next week the plants on sale for 15% off Larissa wants to know the price of the tomato plants if she buys them next week

Answers

Step-by-step explanation:

15%25$

[tex] \frac{15}{100} \times 25[/tex]

[tex] \frac{375}{100} [/tex]

=3.75

25-3.75=21.25$

Find the product of 54 and the sum of 15

Answers

Answer:

6 and 9 are the two numbers that have a sum of 15 and when multiplied + 54

Step-by-step explanation:

translate seven minus three times a number into an algebraic expression

Answers

7 - 3 x X
Key: x is times and X is “a number”

Vicky is a cook at a diner. Before the diner opened, she used 12 eggs to make a large frittata that will be sold by the slice. She will also use 3 eggs whenever someone orders an omelet. If Vicky uses a total of 39 eggs by the end of the day, how many omelets must have been ordered?
Write and solve an equation to find the answer.

Answers

Answer:

6 is this answers to find

Answer:

9 omelets

Step-by-step explanation:

She used 12 eggs in the morning so 39-12= 27 then 27/3 = 9

Hope that helps!

Please solve the math problem for me... I will mark you brainliest

Answers

Answer:

x = 5

Step-by-step explanation:

3x + 1 should equal 16

Answer:

X=5

Step-by-step explanation:

3x+1=16

move the 1 over to the 16 so it is 16 - 1 = 15

3x=15

Move the 3 over to where the 15 is in order to get x by itself

3/3 = x

3/15 = 5

so X should = 5

pa answer po plss plssss

Answers

29/32

Step-by-step explanation:

ng x value 32wrffddfddfffryufcjhfddxhjhddxffdssdtt

NO LINKS IF YOU HAVE LINK DO NOT ANSWER PLEASE ANSWER NO LINKS Please no links will mark brainiest for complete and correct answer.
PLEASE SHOW ALL OF YOUR WORK
Solve for p
3(2p−1)−2(3p+4)=11p

Answers

Answer:

p = -1

Step-by-step explanation:

3(2p - 1) - 2*(3p+ 4) = 11p

Use distributive property: a(b +c) =a*b +a*c

3*2p -3*1 -2*3p + (-2)*4 = 11p

6p - 3  - 6p - 8 = 11p

6p - 6p - 3 - 8 = 11p

          - 11 = 11 p

Divide both sides by 11

     -11/11 = p

p = -1

Giving brainlyest .... .....

Answers

Answer:

4.475 is the answer.

Step-by-step explanation:

also hide your tabs just in case ;)

Answer:

4.475 believe me i did k12 before plz give me brainlyiest explanation:

Help please i need this done by tomorrow

Answers

Step-by-step explanation:

here you go I hope my answer is correct goodbye

Answer:

i think you draw it

Step-by-step explanation:

it tells you the answer

Someone pls help me I will make you brain

Answers

Answer:

base salary

Step-by-step explanation:

f(0) means that he had no sales so the only money made would be from the base salary

May I please receive help?

Answers

Answer:

81+71+x=180

152+x=180

x=180-152

x=28°

Step-by-step explanation:

Hope that this is helpful.

Have a great Day.

HELP PLEASE!!!!

The 10 largest soccer and football stadiums have a capacity of at least of 1 x 105 people. Each stadium has 8 events each year for 10 years.

How many total people attended these events if every event was seated to capacity? Select ALL that apply

A

at least 80,000,000 people

B

at least 800,000,000 people

С

at least 0.8 x 107 people

D

at least 8 x 107

people

E

at least 80 x 107 people

Answers

We have 10 stadiums each holding 105 people.
If each stadium has 8 events each year that’s 80 events per year in total.
So there is 800 events throughout the 10 years (each year holding 80 events).
To find the total number of people that attended the event we multiply the number of people that attended each event by how many events we had in total (105x800=84000)
So, C,D and E apply.

(1/3) to the power of 3
Plz

Answers

Answer:

1/27

have a lovely day <3

Answer:

[tex]\frac{1}{27}[/tex]

Step-by-step explanation:

[tex]\frac{1}{3} ^3[/tex]

[tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex]

[tex]\frac{1}{27}[/tex]

PLS HELP ME WITH THIS! I NEED IT RIGHT NOW!! PLSSS I'LL GIVE BRAINLIEST I PROMISE. JUST PLS HELP ME.

In 2010, an estimated 1.664 x 10⁸dollars in 1000 bills were in circulation. How many 1000-dollar bills were in circulation?​ ​

Answers

Answer:

166,400,000

Got the same one today and figured it out! Yw!❤

A water bucket in your backyard has a small hole in it. You notice that it drained a total of 3.5 liters

in 4 days. What is the average change in water volume each day? (hint: divide)

Answers

In each day the average change in the water volume is 0.875 liters

hello can anyone help?

Harry drives 182 miles.
His average speed is 35 miles per hour.
How long does the journey take?
Give your answer in hours and minutes.

Answers

Answer:

5 hours 12 minutes

Step-by-step explanation:

Amount of time the journey took = 182 miles ÷ 35 miles/h

                                                       = 5.2h

                                                       = 5h 12mins

If 20 apples cost N300 how many apples can be bought for N1875

Answers

Answer:

28125

Step-by-step explanation:

300÷20=15

15×1875=28125

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