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

Can someone help me and if you don’t have the answer don’t answer cause you’re just wasting my time

Answers

Answer: 1 is 534

Step-by-step explanation:

If you receive $68 for mowing lawns for 8 hours. What would be the equation to find out how much money you would receive in an hour?

Answers

Answer:

$68÷8= x money per hour

Step-by-step explanation:

explain and show how please ! and give answer someone pls answer asap !

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Answer:

Both angels are 70 and both added are 140.

Step-by-step explanation:

Because of the rules, that's names i never remember angle 1 and angle 2 are both 70° and obiously they equal 140.

Can someone help me with these two? Please

Answers

For 16/18 it would be 8/9
For 10/15 it would be 2/3

Answer:

8/9 and 2/3

Step-by-step explanation:

find common factor with each of the numbers and divide by that

16 and 18, 2 is the gcf.

16/2=8   18/2=9

the gcf in the second one is 5.

10/5=2  15/5=3

Hope this helps!

5.5.WW3
Question Help
Find the quotient
30)593
Select the correct choice below and fill in the answer box(es) within your choice.
OA. The quotient is
OB. The quotient is
R

Answers

19.7666
Because it just makes since I think

Solve for X then find the measure of

Answers

Answer:

x=11

m<a=80º

m<b=80º

Step-by-step explanation:

They are congruent so

8x-8=5x+25

8x=5x+33

3x=33

x=11

Answer:

Step-by-step explanation:

8x-8=5x+25

8x+5x=25--8

13x=33

x=2.5

x=3cm

What is the value of {-12}
–13
–12
12
13

Answers

Answer: B. -12

Edge 21: Since the brackets are facing down, there is no need to round the -12 because it's already an integer.


[tex]The \: value \: of \: \sqrt{6 + \sqrt{6 + \sqrt{6} + .......... \: to \: \infin } } \: is \: \underline{ \: \: \: \: \: \: \: \: \: \: \: .}[/tex]
CORRECT EXPLANATION WILL BE MARK AS BRAINLIEST.​

Answers

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

Let us assume that:

[tex] \sf \longmapsto x = \sqrt{6 + \sqrt{6 + \sqrt{6 + ... \infty } } } [/tex]

We can also write it as:

[tex] \sf \longmapsto x = \sqrt{6 + x } [/tex]

Squaring both sides, we get:

[tex] \sf \longmapsto {x}^{2} =6 + x[/tex]

[tex] \sf \longmapsto {x}^{2} - x - 6 =0[/tex]

By splitting the middle term:

[tex] \sf \longmapsto {x}^{2} - 3x + 2x - 6 =0[/tex]

[tex] \sf \longmapsto x(x - 3) + 2(x - 3 ) =0[/tex]

[tex] \sf \longmapsto (x+ 2)(x - 3 ) =0[/tex]

Therefore:

[tex] \longmapsto\begin{cases} \sf (x+ 2) =0 \\ \sf (x - 3) = 0 \end{cases}[/tex]

[tex] \sf \longmapsto x = - 2,3[/tex]

But x cannot be negative.

[tex] \sf \longmapsto x = 3[/tex]

Therefore, the value of the expression is 3.

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

Given:

[tex]\sf\longmapsto x=3[/tex]

We can also write it as:

[tex]\sf\longmapsto x = \sqrt{9}[/tex]

[tex]\sf\longmapsto x = \sqrt{6+3}[/tex]

[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{9}}[/tex]

[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+3}}[/tex]

[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{9}}}[/tex]

[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+3}}}[/tex]

This pattern will continue.

[tex]\sf\longmapsto x = \sqrt{6 + \sqrt{6+\sqrt{6+...\infty}}}[/tex]

Which pair of numbers has a sum of 0?
1) 2 and 12
2) 2 and –12
3) 2 and –0.2
4) 2 and –2

Answers

4 because 2 + -2 is 0
The answer is 4) 2 and -2

If you did 2 + - 2, it is equal to 2 - 2 which is 0

if i had 475 cannolis ans a box can only carry 15 how many boxes will i need.​

Answers

Answer:

you would need 32 boxes

Step-by-step explanation:

475/15 = 31.666

32 boxes

475/15=31.7 but you can't get 0.7 boxes so you would need 32 to carry all of the cannolis.

Use synthetic division to find the result when 4x^3+3x^2– 8x – 7 is divided by x+1.

Answers

Answers:

4x^2 - x - 7

please help I will make you Brainliest if correct (show working)​

Answers

1.) X= 4m - 1.2m = 2.8m

Split the irregular shape into 2 (A and B)

A= 4m x 3.8m = 15.2m^2

B= 3m x 2.8m = 8.4m^2

2.) Total area = A + B
= 15.2 + 8.4 = 23.6m^2

ANSWER THIS ASAP PLEASE !

Answers

Simple the answer is: n=14

2n-3=25
We can move the divided by to other side of equal sign and it now because multiply by 5.
2n=28
We add 3 to both sides of equal sign
n=14
We divide 2 to both sides of equal sign to get the variable by itself
Your answer is : n=14

Apply the distributive property:
-3(x+2) =

Answers

Answer:

-3x-6

Step-by-step explanation:

you multiply x by -3 getting -3x then you multiply -3 by positve 2 getting -6

Hello skm413002!

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

Apply the distributive property:

-3(x+2) =

[tex] \large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}[/tex]

By applying the distributive property, we can solve it as....

[tex] \sf \: - 3(x + 2) \\ = \sf \: (- 3 \times x) -( 3 \times 2) \\ = \large \boxed{\boxed{ \bf - 3x - 6}}[/tex]

Method :-Distributive property.

Steps :-Multiply -3 with x & 2.Add the 2 products.You'll get the answer as -3x - 6.

__________________

Hope it'll help you!

ℓu¢αzz ッ

A student performed the following steps to find the solution to the equation
x2 - 2x - 8 = 0. Where did the student go wrong?
Step 1. Factor the polynomial into (x-4) and (x - 2)
Step 2. X-4 = 0 and x - 2 = 0
Step 3. x = 4 and x = 2
A. The student did not make any mistakes, the solution is correct
B. in Step 2
C. in Step 1
D. in Step 3


Answers

Answer:

step 1, c

Step-by-step explanation:

he was wrong in step 1.

when factoring out (x-4) and (x-2), you have to distribute x*x, x*-2, -4*x, and -4*-2

if you do it you get x^2 - 2x -4x + 8

the correct way to factor will be (x-4)(x+2)

when you factor out you will get the original equation you started with.

Help me please i need the equation of axis of symmetry

Answers

Answer:

x = -2

Step-by-step explanation:

It's a vertical line at x = -2

maths help me maths giving 10 point​

Answers

Step-by-step explanation:

[tex]x-2>4[/tex]

[tex]x>6[/tex]

And

[tex]3x+1\leq 28[/tex]

[tex]3x\leq 27[/tex]

[tex]x\leq 9[/tex]

So [tex]x[/tex] ∈ [tex](6, 9][/tex]

Please give me a brainliest answer

b(n)=−4−2(n−1)

find the 12th term in the sequence.

Answers

Answer:

-18

Step-by-step explanation:

b(12) = 4 - 2(12-1)

= 4 - 2(11)

= 4 - 22

= -18

if 3x - 2y = 9 , 27x³- 8y³= 1377 , prove that xy = 4



plzz answer this question... ​

Answers

Step-by-step explanation:

Here we are given that , the Value of

[tex] 3x - 2y = 9 [/tex] [tex] 27x^3 - 8y^3 = 1377 [/tex]

And we need to find the prove that ,

[tex] xy = 4 [/tex]

We know a identity as ,

[tex] (a-b)^3 = a^3-b^3-3ab(a-b) [/tex]

On cubing both sides of the given equation,

[tex] (3x-2y)^3 = 9^3 [/tex]

Simplify and then substitute ,

[tex] 27x^3-8y^3 -3(3x)(2y)(3x-2y ) = 729[/tex]

[tex] 1377 - 18xy (9) = 729 [/tex]

[tex] 162xy = 1377-729 [/tex]

[tex] xy =\dfrac{648}{162}[/tex]

[tex]xy = 4 [/tex]

Hence Proved !

PLEASE HELPP!! Type an equation for the
following pattern. Make sure
the fraction is in simplest form.

Answers

Answer:

y = -3/2x + 10.5

Step-by-step explanation:

You can plug in the x values and you'll get the y values of the table. Hope this helps :)

Is it possible to list all the fractions between 2 and 3? Explain.

Answers

Answer: No

Step-by-step explanation:

There are infinitely many numbers. Numbers so big that they are beyond our comprehnsion. Numbers can also be infinitly small. A fraction is something less than a whole. So the answer is no you can't list them all.

Solve for x 3/8(2x+16)−2=13

The "/" is for a fraction btw

Answers

X= -623/96


I hope this helped

will give BRAINLIEST!!!!!!
3 3/4 X 1 2/5 do a step by step explanation please and also you have to make it so you convert it into an improper fraction first... please answer!!!

Answers

Answer:

5 1/4

Step-by-step explanation:

To convert into an improper fraction, we times the whole number by the denominator and then add the numerator. For the first number, it is 15/4 and the second number is 7/5. Then we multiply 15/4 and 7/5 to get 5 1/4.

Answer:

99/5

Step-by-step explanation:

CONVERT INTO:

33/4 x 12/5

MULTIPLY THE FRACTIONS:

(33x12)

--------------

5

CANCEL TERMS:

(33x3)

-----------

5

SIMPLIFY:

99/5

what is the sign of a • (-b/b) when a = 0 and b < 0?

Answers

Answer:

gimmie my points boi

Step-by-step explanation:

eiurfh4iewurhfwo8rho

3(x+1)=2(x-3) whats the answer

Answers

The answer is -9

I dont know the step-by-step used a calculator

Jerry played with 3 friends today, all at different times. He played with Tommy for 1 7/8 hours, then Nathan for 1 3/4 hours, then Chris for 3/2 hours.
How many hours did Jerry play with his 3 friends today?

Answers

Answer:

4hrs 7 minutes and 30 seconds

Step-by-step explanation:

1 7/8 = (1=60) + (7/8 * 60) = 1 : 52:50 time played with Tommy   1 3/4 = (1=60 ) ( (3/4 * 60) = 1:45:00 time played with Nathan   3/2 = (3/2 *60) = 90 = 1:30:00 time played with Chris    Total played with 3 friends = 1:52:50 + 1:45:00+1:30:00= 4:07:50 = 4hrs 7 minutes and 30 seconds

Can you translate the measurements to (cups, teaspoons, tablespoons etc.)

Top flour 170g
Baking powder 5g
Sugar 10g
Butter 40g
Maple syrup 30ml
Milk 40ml

Answers

Answer:

Flour: 18.76 Tablespoons

56.28 Teaspoons

1.17 U.S. Cups

Baking Powder: 0.35 Tablespoons

1.04 Teaspoons

0.02 U.S. Cups  

Sugar: 0.80 Tablespoons

2.40 Teaspoons

0.05 U.S. Cups

Butter: 2.82 Tablespoons

8.46 Teaspoons

0.18 U.S. Cups

Maple Syrup:

0.127 Cups

2.029 Tablespoons

6.087 Teaspoons

Milk:

0.169 Cups

2.705 Tablespoons

8.115 Teaspoons

Hope this helps!!

Have A Blessed Day <333

Select the correct answer.
Which statement is true about the graph of this equation?

y + 4 = 4(x + 1)

A.
The graph is a line that goes through the points (1,-4) and (0,0).
B.
The graph is a line that goes through the points (1,4) and (2,8).
C.
The graph is a line that goes through the points (-4,-1) and (-3,-3).
D.
The graph is a line that goes through the points (4,1) and (5,5).

Answers

The answer is B
I hope this helped you !!

Answer:

A

Step-by-step explanation:

The graph is a line that goes through the points (1,-4) and (0,0)

Write the prime factorization of 42. Use exponents when appropriate and order the factors from least to greatest

Answers

42: 2,3,7
2 x 3 x 7 = 42

Answer:

42 = 2*3*7

Step-by-step explanation:

42 can be rewritten as 2*21, for example.  

2 is prime.  21 = 3*7.

Then 42 = 2 * 21 is also equal to:

         42 = 2*3*7. where these factors are ordered from least to greatest.  The prime factors of 42 are {2, 3, 7}.

3. Which table has a constant of proportionality equal to 2.5?
x
х
y
X
0
0
2.5
os
2.5
NO
1
2
.
5
7.5
А
о
B
х
y
2
у
2.5
3.75
W NX
2
5
3
3
7.5
10
4
ch
5
4
D

Answers

Answer:

your answer is A

I can assure you that you will give brainlest

Answer:

A

Step-by-step explanation:

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