find the real numbers x&y so that (x^2+2xy)+i(y-1) = (x^2-2x+2y) - i(x+y)​

Answers

Answer 1

In order for two complex numbers to be equal, their real and imaginary parts must match up.

So if

x ² + 2xy + i (y - 1) = x ² - 2x + 2y - i (x + y)

then

x ² + 2xy = x ² - 2x + 2y

and

y - 1 = -x - y

Solve for x and y : the first equation gives

x ² + 2xy = x ² - 2x + 2y

2xy = 2y - 2x

and the second gives

y - 1 = -x - y

2y = 1 - x

Substitute this into the first equation:

x (1 - x) = (1 - x) - 2x

x - x ² = 1 - 3x

x ² - 4x + 1 = 0

x = 2 ± √3

Then

x = 2 - √3   ==>   y = (-1 + √3)/2

x = 2 + √3   ==>   y = (-1 - √3)/2

both of which make both sides of the equation (2 - √3) + i (√3 - 3)/2.


Related Questions

NJ Transit raises its train fees. Snooki wants to visit her parents which used to cost $28 but they increased the fares by 15%. What will the ticket cost now?

Answers

Answer: 32.20$ Train Fee

Step-by-step explanation:

15% of 28 is 4.20... 4.20 will be added to the current Train Fee

   28.00$

 +   4.20$

    32.20$

Final result: The Train Fee will be 32.20$

4. In a class of 35 students, 20 offer Physics,
18 offer Chemistry and 2 offer neither
Physics nor Chemistry
1) Illustrate the information on a Venn
diagram
il) How many students offer all the two
subjects?
1) How many students offer Physics!
1) How many students offer only one
subject

Answers

5 students offers all the two subjects.

Student that offers Physic only = 15 students

Student that offers chemistry only  = 13 students

Students that offers only one subject = 28 students

How to solve a Venn diagram?

Total student in the class = 35

20 offer physics.

18 offer chemistry

2 offer neither physics nor chemistry.

Therefore,

x = student that offer both subject

35 = 20 + 18 - x + 2

35 - 2 - 20 - 18 = -x

-5 = -x

x = 5

Therefore, 5 students offers all the two subjects.

Student that offers Physic only = 20 - 5 = 15

Student that offers chemistry only = 18 - 5 = 13

Students that offers only one subject = 13 + 15 = 28

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#SPJ1

h(1) = 9
h(2) = 3
h(n)=h (n−2) ⋅ h(n−1)
​h(3)

Answers

Answer:

27

Step-by-step explanation:

h(n)=h (n−2) ⋅ h(n−1)

h(3)=h (3−2) ⋅ h(3−1)

h(3)=h (1) ⋅ h(2)

h(3)=9 ⋅ 3

h(3)=27

Answer:

27

Step-by-step explanation:

khan

Jace recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 11
Bass 14
Drums 11
Keyboard 14
Eighth Grade Students
Instrument # of Students
Guitar 13
Bass 13
Drums 8
Keyboard 3

Based on these results, express the probability that a seventh grader chosen at random will play an instrument other than bass as a percent to the nearest whole number.

Answers

The probability that a seventh grader chosen at random will play an instrument other than bass is 72%.

Let A={5,8}, B={p,q}, C={r,v} How many elements are in A×B?

Answers

There are 4 elements in the set A* B

How to determine the number of elements in A * B?

The sets are given as:

A={5,8}

B={p,q}

C={r,v}

The expression A * B implies that:

A * B = n(A) * n(B)

Where n( ) implies that the number of elements in......

So, we have

A * B = 2 * 2

This is so because sets A and B have 2 elements each

Evaluate the product

A * B = 4

Hence, there are 4 elements in the set A* B

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Apply the distributive property to factor out the greatest common factor.
40f + 30

Answers

It is 30 because everyone is

The cube of an integer is called a __________ ?

Answers

Answer:

a perfect cube

Step-by-step explanation:

Answer:

It is called a perfect cube .

Step-by-step explanation:

a person runs at a constant speed of 9.2 miles per hour for 6 minutes and 30 seconds. How far did they travel in yards.

Answers

Given:

Speed[tex]= \bold{9.2 \ \frac{miles}{hour}}[/tex]  

[tex]\therefore \\\\[/tex]

1-hour= 60 minutes

1-minutes=60 second

So

1-hour= 3600 second

Converting the given time into seconds:

Time= 6 minutes and 30 second

       [tex]=\bold{6\times 60 \ second + 30 \ second }\\\\=\bold{360\ second+30\ second}\\\\=\bold{390\ second}\\\\[/tex]

When 3600 seconds covers=9.2 miles

Then equation:

[tex]=\bold{\frac{9.2}{3600}}\\\\[/tex]

390 seconds covers:

[tex]=\bold{\frac{9.2}{3600}\times 390 \ miles} \\\\[/tex]  

Let

[tex]\bold{1 \ miles= 1760\ yard}\\\\[/tex]

Convert the traveling value into yards:

[tex]=\bold{ \frac{9.2}{3600}\times 390\times 1760}\\\\=\bold{ \frac{9.2}{36}\times 39\times 176}\\\\=\bold{ \frac{9.2}{12}\times 13\times 176}\\\\=\bold{ \frac{9.2}{12}\times 2288}\\\\=\bold{ 9.2\times 190.66}\\\\=\bold{ 1754.072\ yards}\\\\[/tex]

Therefore, total traveling yards are"1754.072".  

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Speed of the person has been given as 9.2 miles per hour.

Therefore, speed of the person in miles per minute = [tex]\frac{9.2}{60}[/tex]

Duration for which the person is running = 6 minutes and 30 seconds

                                                                    = 6 minutes and [tex]\frac{30}{60}[/tex] minutes

                                                                    = 6.5 minutes

Since, Distance = Speed × Time

By substituting the values in the expression we can get the distance traveled.

Distance = [tex]\frac{9.2}{60}\times 6.5[/tex]

               = 0.9967 miles

Since, 1 mile = 1760 yards

Therefore, 0.99667 miles = 1760 × 0.99667

                                           = 1754.13 yards

Total distance traveled by the person is 1754.13 yards.

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Carlo got a pet snake as a birthday present. On his birthday, the baby snake was just 26 cm long. He has been measuring its length weekly and has noticed that it has been growing approximately 2 cm each week.

Write an equation to represent the length of the snake in weeks since Carlo's birthday use L for length and w for weeks.​

Answers

The equation to represent the length of the snake in weeks:

[tex]L=2w+26[/tex]

Given:

A snake of lenght of 26 cemtimeters grows approximately 2 centimeter long each week.

To find:

The equation to represent the length of the snake in weeks

Solution:

Let the length of the snake in' w' weeks be 'L'.

The initial length of the snake on Carlo's birthday = 26 cm

At starting very first week the length of the snake was 26 cm. And after a week the lenght of the snake becomes 28 cm and then aftertwo weeks the length becomes 30 cm and so on.

Increase in length of the snake each week = 2 cm

And increase in length of the snake in 'w' weeks = (2×w) cm

And the length of the snake in terms weeks (w) will be given by equation:

[tex]L=2\times w+ 26\\L=2w+26[/tex]

The equation to represent the length of the snake in weeks:

[tex]L=2w+26[/tex]

Learn more about equation representation here:

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Please give this in steps

Answers

Answer:

(x - y)²

Step-by-step explanation:

Given

(x + y)² - 4xy

= x² + 2xy + y² - 4xy

= x² - 2xy + y²

= (x - y)²

Answer:

[tex] {(x + y)}^{2} - 4xy = {x}^{2} + 2xy + {y}^{2} - 4xy \\ = {x}^{2} - 2xy + {y}^{2} \\ = {(x - y)}^{2} \\ thank \: you[/tex]

Can anyone help? Most brainiest for the correct answer!!

Answers

Answer:  25

Explanation:

The "large cars" pie slice takes up 7% of a full circle. This means that the degree measure of this slice takes up 7% of a full 360 revolution.

7% of 360 = 0.07*360 = 25.2 degrees

This then rounds to 25 degrees

25

If you like, I can put on the solution.

If X= 9 and Y = 3, what is XY

Answers

Answer:

The most basic question I have ever seen lol

XY = 9*3 = 27

It is 27

XY means X*Y
3*9=27

PLZ HELP ME I NEED HELP PLZZZ!!!!!
Select all that apply.

Given the points (-6, 8) and (-3, 4), which of the following are true about the line passing through these points?

The line represents a direct variation function.
The line has a slope of -3/4 .
The point (9, -12) is also on the line.
The line has a slope of 3/4 .

Answers

Answer:

the point (9,-12) is also on the line

Step-by-step explanation:

by using the 2 points the equation is y=-4/3x

use x of 9

y = -12

it will also represent a direct variation function

so two of the 4 will be correct

Answer:

The point (9,-12) is also on the line

Step-by-step explanation:

Please give brainliest

What is the perimeter (in feet and inches) of a rectangle that has a length of 12'7" and a height of 11'3"?

Answers

Answer:

p=2l+2w

=2*12'7"+2*11'3"

Hours worked in a week - 32; Total Pay - $160.00; What is the hourly rate?

Answers

Answer:

$5

Step-by-step explanation:

Number of hours worked = 32

Total pay = $160

So, hourly rate

= Total pay/number of hours worked

= $160/32

= $5

find the domain of f(x) = 3x + 5

Answers

Answer:

All real numbers

Step-by-step explanation:

All real numbers: f(x) is defined for all values of x. There are no discontinuities or places where f(x) is undefined. f(x) is just a straight line going to infinity.

Answer:

(-infinity, infinity), or all real numbers

Step-by-step explanation:

If you were to look at it graphically, it would be a linear function with a slope of 3 and shifted up 5 units. (i attached a screenshot of what the graph would look like at the bottom :)

since there are no domain restrictions, you're not really going to have any issues or gaps which is when you might need to do something like

(-infinity,4] u(5,inifinity) --> since this isn't the case though, you're totally free to just write all real numbers, because all real numbers in the x-plane (as that is what domain looks at) are included.

When all else fails, (at least for homework), desmos is great for graphing and looking at everything visually

Hope that helps! lmk if you have any questions :)

Q16. If the perimeter of a rectangular house is 25 1/3 yards, and the length is 22 feet. What is the
width?
16 feet
O 35 feet
O 37 feet
0 40 feet
42 feet

Answers

Answer:

OPTION A :16 FEET

PERIMETER =26 1/3=76/3yard=76/3×3=76 feet

LENGTH=22feet

Width=76/2-22

WIDTH=38-22=16 FEET

please help me to do this question ​

Answers

Answer:

firdt method is

Length x breath

is equal to ½

Build a function whose domain is all real numbers other than -4, and whose range is all real numbers other than 5.

Answers

Answer:

An example is the rational function [tex]y=\frac{5x}{x+4}[/tex].

Step-by-step explanation:

The graph of the rational function [tex]y=\frac{5x}{x+4}[/tex] has a vertical asymptote at x = -4 where the denominator is equal to zero.  The function is undefined there, so the domain is all real numbers except -4.

The graph has a horizontal asymptote  y = 5  so the domain is all real numbers except 5.

See the attached image for the graph of the function (purple) and it's vertical asymptote (black).

8th grade math
5. What is the probability of rolling a 3 on a 6-sided number cube and then NOT rolling 2 or 4 on a 6-sided number cube?

Answers

Answer:

5 in 12 chance or 42% probability of happening

Probably of rolling 3 is 1/6
Probably not rolling 2 or 4 is 4/6
Independent event so:
P(a)*P(b)= 1/6*4/6 = 4/36 =0.111

2. 3.6 x 5.5? Explain your answer. (Make sure you include how you knew where to
place the decimal point.)

Answers

Answer:

19.80 or 19.8

Step-by-step explanation:

When multiplying decimal numbers we forget the decimal points and multiply normally; like, 3.6 x 5.5 = 1980, then we count how many decimal numbers(numbers after the decimal point) there are in the factors(In 3.6 we have the decimal number 6. And in 5.5 we have the decimal number 5 ). So here we have 2 decimal numbers resulting in our answer being, 19.80 or 19.8 since the 0 is unnecessary.

In a mathematics class , half of the students scored 84 on an achievement test. With the exception of a few students who scored 50 , the remaining students scored 76. Which of the following statements is true about the distribution of scores ?


A. The mean is greater than the mode.
B. The mean and the median are the same.
C. The mean is less than the median.
D. The mean is greater than the median.

Answers

Answer: B. The mean is less than the median

Step-by-step explanation:

there are some that scored 51 which means - mean<median

Find the AREA of the shape​

Answers

Step-by-step explanation:

LxB

8x7

equals :56

Area equals to 56cm

X¹² - 1 แยกตัวประกอบของพหูนาม

Answers

Answer:

[tex]\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)[/tex]

Step-by-step explanation:

Factor of [tex]x^{12}-1[/tex] is

[tex]\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^4-x^2+1\right)[/tex]

PLZ HELP ASAP I NEED PLZZZ!!!!!!
Fill in the blank with the correct response. The slope of the graph of y = -2/3x is __.

Answers

Answer:

Solution given:

Equation of line is:

y=-⅔x

comparing above equation with

y=mx+c

we get

m=-⅔

So

slope is -⅔

Answer:

slope is -2/3

Step-by-step explanation:

I. It's linear equation

    y = mx + b

when y is output, x is input, m is slope and b is addition.

The statment above is y = -2/3x + 0

So -2/3 is slope or m.value

Hope that help :D

Type your answers into the boxes.
The ratio of men to women in a gym is 7 : 5
What fraction of the gym members are women?

Answers

Answer:

[tex] \frac{5}{12} [/tex]

Step-by-step explanation:

[tex] \frac{5}{7 + 5} [/tex]

I'm not sure about the answer. Sorry if it's wrong.

in a class of 80 students in Debre Berhan university,45 good in mathematics,15 are good in both Mathematics and English,13 are good in both Mathematics and Psychology, 16 are good in both in English and psychology,20 are good in Psychology and 9 are good in both of the three courses A,how many students are good in mathematics only? B,how many students are not good in any of three courses?

Answers

The relationship between the number of students that are good at a given subject is an illustration of sets.

26 students are good at Mathematics only.28 students are not good at all.

We use the following representations:

[tex]M \to[/tex] Mathematics

[tex]E \to[/tex] English

[tex]P \to[/tex] Psychology

From the question, we have the following parameters

[tex]M = 45[/tex] -- Mathematics

[tex]M\ n\ E =15[/tex] -- Mathematics and English

[tex]M\ n\ P =13[/tex] -- Mathematics and Psychology

[tex]E\ n\ P =16[/tex] -- English and Psychology

[tex]P=20[/tex] -- Psychology

[tex]All = 9[/tex] -- All 3 subjects

[tex]Total = 80[/tex] -- All students

The number of students that are good at mathematics only is as follows:

First, we calculate those that are good at mathematics and English only

[tex](M\ n\ E)' = M\ n\ E - All[/tex]

[tex](M\ n\ E)' = 15 - 9 = 6[/tex]

Then those that are good at mathematics and psychology only

[tex](M\ n\ P)' = M\ n\ P - All[/tex]

[tex](M\ n\ P)' = 13 - 9 = 4[/tex]

So, the students that are good at mathematics only are:

[tex]M' = M - (M\ n\ E)' -(M\ n\ P)' - All[/tex]

[tex]M' = 45 - 6 -4 -9[/tex]

[tex]M' = 26[/tex]

Hence, 26 students are good at Mathematics only.

To calculate the number of students that are not good in any of the subjects, we make use of the complement rule

[tex]A + A' = Total[/tex]

Where:

[tex]A \to[/tex] Students that are not good in any

[tex]A' \to[/tex] Students that are good in at least one

So, we have:

[tex]A' =M' + (M\ n\ E)' + (M\ n\ P)' + (E\ n\ P)' + All[/tex]

Where:

[tex](E\ n\ P) = (E\ n\ P)' - All[/tex]

[tex](E\ n\ P) = 16-9 = 7[/tex]

The equation becomes:

[tex]A' =26 + 6 + 4+7+9[/tex]

[tex]A' =52[/tex]

Recall that:

[tex]A + A' = Total[/tex]

[tex]A = Total - A'[/tex]

[tex]A = 80 - 52[/tex]

[tex]A = 28[/tex]

Hence, 28 students are not good at all.

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A=1/2bh solve for b then h

Answers

Answer:

There is no right or wrong answer

Step-by-step explanation:

You did not give enough information, this formula usually comes with a triangle that you want to solve, therefore no one can answer this correctly since there is nothing to solve.

The question is asking your to restate b in terms of A and h.

A = 1/2 bh

divide by 1/2
2A = bh

divide by h
2A/h = b

Sarah is going to pay for an item using gift cards. The clerk tells her tht she will need 2 gift cards and as additional $3 to pay for the item.

Write an algebraic equation to find the cost for any amount of gift cards

Answers

Answer:

Step-by-step explanation:

t=2g+3.

What is the solution to
:-7?
A. 81
B. 63
C. 63
D. -81

Please help me I’m dum

Answers

Answer:

-63

Step-by-step explanation:

63/9 = 7, so in order to make the answer -7, 63 must be negative.

Other Questions
:) Who is good at english please help me answer my question For each of the past years, Perdana and Kadita have spent their vacation time at home, either working in garden or fixing up the house. This year, however, they are planning to spent their end of the year vacation somewhere else. They have checked the internet for weather information about areas of teh country the might like to visit. They are really eager to travel somewhere soon. In fact, if they had free time right now, they would take the vacation immediately, but they cant leave right now. They still have a couple of months to explore theiroptions. So far, they have searched much information, but most of it does not satisfy them since they want to go to country sides. If the wanted to spent their near the water, they would have a hard time choosing among dozens of outstanding beach resorts. For example, if they went to the beach in Bali, they would not like the weather in that month-it will be raining most of the time. Thats very dissapointing for them. On the other hand, if tehychoose to visit singapore beach in December, both the air and the water temperatures would be considerably cold,around 20 degrees. Thats sounds frustating to them. Perdana and Kadita also like to go camping, so vocationing in the mountain is another option. They could choose to visit Ciperna in Cirebon if they wanted warmer weather. In December, the temperature in Cirebon can range from a high of 45 degrees to a low of 35 degrees. If they went to cirebon, they would certainly have to encounter the risk of landslide. It is without a doubt a tough decision that Perdana and Kadita are facing. They wish they were able to go to all of the places they have researched. If they had more money and more time, they would be able to do exactly that. In fact, they would go to both the country side and the beaches this year if they had enough money. Unfortunately they have spent it to buy a new car.1. What is the passage about? a. Planning upoming vacation b. Enjoying a great vacation c. Regretting previous vacation d. Negotiating the next vacation e. Cancelling fascinating vacation 27.2. Why cant Perdana and Kadita leave for vacation now?a. They have to spend their vacation tie at home b. They are working in the garden c. They are fixing up the house d. They do not have free time e. They are hardly eager to travel somewhere 28.3. Perdana and Kadita do not intend to spend their next vacation time near the water because____ a. It is difficult to choose among dozens of outstanding beach resorts b. They have visited many outstanding beach resorts c. It will be too crowded in Bali d. They do not likle swimming and surfing e. It is always nice to lie on beach 4. Perdana and Kadita skip singapore beaches from the list____ a.Because both the air and water temperatures are not cold enough b. Because of considerably cold air and water temperatures c. Due to hectic working schedule d. Since they do not like bad destination e. Owing to the insufficient amount of money5. According to the passage, Ciperna____a. Has fertile lands b. Has cool water c. Is a mountains area d. Is very close to cirebon e. Has average temperature between 35 degrees to 45 degrees throughout the year6. Unless Perdana and Kadita spent the money to buy new car, they___ a. Would not be able to go to all of the places they have researched b. Would be able to go to singapore c. Would go to both the countryside and the beaches this year d. Would not have enough money to take a vacation e. Would spend too much ion travelling. 7. Were Perdana and Kadita to want warmer weather __a. They could choose to visit Cipema in Cirebonb. they would certainly have to encounter the risk of landslide c. they would go campingd. the air and the water tempratures would be considerably cold e. they would have a couple of months to explore the area8. Planning the upcoming vacation______ a. Is tough decision for Perdana and Kadita b. Makes Perdana and Kadita excited c. Creates frustation for Perdana and Kaditad. Dissapoints both Perdana and Kadita e. Takes Perdana and Kadita a couple of months A worker earns the same amount for eachhour. If he earned $48.00 in 3 hours, howmuch would he earn in 8? In 40? find the midpoint of R(5,3) and S(-4,6) PLEASEEE What do you know about the company/organization you wish to work for? Help please answrr and read it there are 78.1 grams of carbon in a sample of 92.7 grams of octane. what is the percent of carbon within the sample of octane? kevin buys cornflakes for 1.40 and chocolate for 1.50 he makes cornflakes cakes he sells 10 for 1 each how much profit does he get can 0.462 be written as a fraction and is it a terminating or repeating decimal For each set of measurements, decide whether or not it is possible to draw a triangle with those measurements. If it is possible, draw the triangle.a. Side lengths 2 cm, 3 cm, and 4 cmb. Side lengths 2 cm, 3 cm, and 6 cmc. Angles 90 degrees, 45 degrees, and 45 degreesd. Angles 90 degrees , 60 degrees, and 60 degrees Complete the statement below about developing technology responsibly. To develop technology responsibly, people must evaluate both the ____________ and the____________ consequences of the technology Answer the following qustions How did Jonas Salk die? PLS TELL ME HOW THIS TRICK WORKED!! I HAVE TO SUBMIT KT SOON! an advertisement should containa) name of the product / brand / outlet b) appealing images c) address with information d) all these three A ________ is a statement that is usually true based on the facts available.Which word is it?Look at the photo 2. What can you infer through the juxtaposition the artist creates in Visual Text 2? What messagedoes it send to the viewer? Anyone to help me solve this question. Am going to give brainliest Whats the answer???? The event above best demonstrates which feature of the American way of life? A) The First Amendment guarantees personal freedoms B) The Declaration of Independence asserts the principle of popular sovereignty C) The U.S. Constitution establishes the structure of the federal government D) The Fifth Amendment protects the rights of the accused a rectangular hall room is 12.25 metres in length and 7.75 metre in breadth. find the area of the rectangular hall room.