What is the product of complex conjugates? The product of complex conjugates is a difference of two squares and is always a real number. The product of complex conjugates is the same as the product of opposites. The product of complex conjugates may be written in standard form as a+bi where neither a nor b is zero. The product of complex conjugates is a sum of two squares and is always a real number.

Answers

Answer 1

Answer:

Last given option is the correct answer:

"The product of complex conjugates is a sum of two squares and is always a real number."

Step-by-step explanation:

The product of two conjugates can be described and solved like this:

[tex](a + b\,i) \,(a - b\,i)= a^2-a\,b\.i+a\,b\,i-b^2\,i^2=a^2+0-b^2\,(-1)= a^2+b^2[/tex]

so, no matter what the values for the real values a and b are, the product is always a real number and the sum of two squares.

Answer 2

Answer:

(a + bi)(a – bi) = a2 – (bi)2 = a2 + b2

The product of a complex number and its complex conjugate is

✔ always

a real number.


Related Questions

If y=3/5x+26 find the value of y when x=12

Answers

Answer:

46

Explanation

y = 3 /5x +26

y =?

X= 12

y=3 /5x + 26

y= 3 / 5 × 12 + 26

y = 3 / 60 + 26

y = 20 + 26

y = 46 ans

does anyone know this?

Answers

Answer:

[-10, 3]

Step-by-step explanation:

Hello!

To find the range of a graph you look at the lowest point and the highest point

The highest point is 3

The lowest point is -10

The range is [-10, 3]

Hope this helps!

Answer:

-10, 3

Step-by-step explanation:

high: 3

low: -10

the order of the 2 coordinates goes left or right, then up or down

( plz mark me as brainliest, that would be most appreciated! )

(6+a) divided by 5 -2

Answers

Answer:

(6+a)/3

Step-by-step explanation:

(6+a)/5-3

5-3=2

(6+a)/2

you will use 2 operations when doing algebra. true or false

Answers

Answer:true

You will be using 2 operations

Simplify the following expression: 4(y + 3) − 6(y − 2) + 5

Answers

Answer:

-2y +29

Step-by-step explanation:

Answer:

-2y+29

Step-by-step explanation:

please help on 19 and 20

Answers

Answer:

c and d

Step-by-step explanation:

Answer:

C AND D

Step-by-step explanation:

HOPE I HELPED

PLS MARK BRAINLIEST  

DESPERATELY TRYING TO LEVEL UP

✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                     PEACE!

Solve |2x - 5| = 4 I dont know what you solve for

Answers

Hello!

Answer:

[tex]\huge\boxed{x = 1/2, 9/2}[/tex]

|2x - 5| = 4

Solve for the negative and positive expressions:

2x - 5 = 4

2x = 9

x = 9/2

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

-(2x - 5) = 4

-2x + 5 = 4

-2x = -1

x = 1/2.

Therefore, the solutions are x = 1/2 and 9/2.

How can I identify witch of those numbers don’t belong with the other there 50.1 -50 over two -50.1 square root of 50?

Answers

I'm assuming you were given these four values

50.1,  -50/2, -50.1, sqrt(50)

where 'sqrt' stands for 'square root', and the slash symbol means divide or fraction.

If my assumption is correct, then the term that does not belong is sqrt(50). This is because the other values are all rational. We can express them as a fraction of two whole numbers

50.1 = 501/10-50/2 is already a fraction, no need to do any work for this one-50.1 = -501/10

But we can't do the same with sqrt(50). It is irrational. Note how 50 is not a perfect square. Your calculator will show that sqrt(50) = 7.07106781186548 and that decimal sequence goes on forever without any pattern. If you were given sqrt(49), then it would work because sqrt(49) = 7 = 7/1.

find a9 if the geometric sequence is: 567,-189,63

Answers

Answer:

3720087

Step-by-step explanation:

Given that,

A geometric sequence : 567,-189,63

First term is : 567

Common ratio : 567/-189 = -3

The nth term of a GP is given by :

[tex]a_n=ar^{n-1}[/tex]

n = 9

So,

[tex]a_9=567\times (-3)^{9-1}\\\\a_9=3720087[/tex]

So, the 9th term of the geometric sequence is 3720087.

What is the slope of a line between (-17,6)and (-18,11)

Answers

Answer:

m = -5

Step-by-step explanation:

m = (y₂ - y₁) / (x₂ - x₁)

m = (11 - 6) / (-18 - ( -17))

m = 5 / (-18 + 17)

m = 5 / -1

m = -5

(x+4) (x+10)
simplify​

Answers

Answer:

x^2 + 14x + 40.

Step-by-step explanation:

(x+4) (x+10)

= x(x + 10) + 4(x + 10)     ( By the Distributive Law)

= x^2 + 10x + 4x + 40

= x^2 + 14x + 40.

Answer:

x^2+14x+40

Step-by-step explanation:

xx+x*10+4x+4*10= xx+10x+4x+4*10

Then simplify

x^2+14x+40

I hope this helps!

Please help! ASAP!!! C:

Answers

Answer:

Equation: 5.88/3=p-0.75

The original price for apples was $1.21

Step-by-step explanation:

Equation explanation:

$5.88 divided by 3 pounds of apples = the original price per pound - the $0.75 increase in price

$5.88 for 3 pounds of apples

we divide 5.88 by 3 to see how much money it was per pound

5.88/3=1.96

subtract 1.96 from the price increase of .75

1.96-.75=1.21

A church spire casts a shadow on the level ground. At the tip of the shadow, the tip of the spire lies 25° upward. Walking 100 m closer, the tip of the spire is at an angle of 55°. What must be the height of the spire in Figure 2?

Answers

Answer:

The height of the spire must be 69.24 m

Step-by-step explanation:

The information given are;

The initial angle of elevation of the tip of the spire from the tip of the shadow = 25°

The  angle of elevation of the tip of the spire from the tip of the shadow after moving 100 m closer = 55°

The change distance moved closer to the church spire = 100 m

Let the base angles of the triangle formed by the two rays of the tip of the spire to the tip of the shadow be 25° and ∠x°

We have;

∠x° and the 55° angle of the ray from the tip of the spire to the tip of the shadow are supplementary angles (angle on a straight line)

Therefore;

∠x° = 180° - 55° = 125°

The calculated angle 125° above, the given 25° and the angle in between the two rays from the tip of the spire to the tip of the shadows are the interior angles of the triangle formed by the two rays of the tip of the spire to the tip of the shadow

Let the angle in between the two rays from the tip of the spire to the tip of the shadows = y

Therefore;

125° + y° + 25° = 180 (Angle sum theorem)

y° = 180° - (125° + 25°) = 30°

By sin rule, we have;

100/(sin (30°)) = (The length of the initial ray from the tip of the spire to the tip of the shadow before the shift)/(sin(125°))

Let the length of the initial ray from the tip of the spire to the tip of the shadow before the shift = l

100/(sin (30°)) = l/(sin(125°))

l = (sin(125°))×100/(sin (30°)) = 163.83 m

The height of the spire, by trigonometric ratio = sin(25°) × 163.83 m = 69.24 m

The height of the spire = 69.24 m.

Od=125
d) f = 120
11. Melissa is buying a sweater. The original cost of the sweater
is $18.00. The sweater is 15% off, and sales tax is 8%. How
much will the sweater cost?
a) $14.08
O b) $12.24
O c) $16.52
O d) $15.30

Answers

Answer:

Hey there!

The sweater is selling for 85% of the original price

0.85(18)=15.30

1.08(15.30)=16.52

Let me know if this helps :)

The solution is Option C.

The total cost of the sweater is $ 16.52

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the original cost of the sweater be = $ 18

Let the sales tax percentage be = 8 %

Let the discount of the sweater be = 15 %

So , the equation for the total cost of the sweater is

The cost of the sweater after discount of 15 % is = original cost of the sweater - discount of the sweater x original cost

The cost of the sweater after discount of 15 % is = 18 - ( 15/100 ) x 18

                                                                                = 18 - 0.15 x 18

                                                                                = 18 - 2.7

                                                                                = $ 15.3

Now , the cost of the sweater after sales tax of 8 % is = cost of the sweater after discount + sales tax percentage x cost of the sweater after discount

So , the equation is

The cost of the sweater after sales tax of 8 % is = 15.3 + ( 8/100 ) x 15.3

                                                                                = 15.3 + 0.08 x 15.3

                                                                                = 15.3 + 1.224

                                                                                = $ 16.524

Hence , the total cost of the sweater is $ 16.52

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ2

Bottle A can hold 3L more juice than bottle B. Bottle D can hold 5L more juice than bottle A. Bottle C can hold 3L less juice than bottle A.

Answers

Answer:

This may be incomplete, i will try to answer this in a general way.

We have 4 bottles, A, B, C and D.

If A is the volume of Bottle A, B is the volume of bottle B, C is the volume of bottle C, and D is the volume of bottle D, we have that:

A = B + 3L.

D = A + 5L

C = A - 3L.

Let's solve this system the most we can (we can not fully solve the system because we have more variables than equations)

First, taking the third equation and adding 3L in both sides, we have:

C + 3L = A.

This is equivalent to the first equation, so we have that C = B.

now, we have two equations:

A = B  + 3L

D = A + 5L

We can replace the first equation into the second equation and get:

D = A + 5L = (B + 3L) + 5L = B + 8L

So bottle D can hold 8L more juice than bottle B (and because bottle B and bottle C have the same volume, bottle D can hold 8L more juice than bottle C)

Now, we can order the bottles depending on the volume:

Bottle D is the one with larger volume.

Bottle A comes next.

Bottles C and B are the smaller ones, and they are together because they have the same volume.

what is mid point theorem​

Answers

Answer:

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

Step-by-step explanation:

i don't have an explanation though

Answer:

The theory of midpoint theorem is used in coordinate geometry stating that the midpoint of the line segment is an average of the endpoints. Both the ‘x’ and the ‘y’ coordinates must be known for solving an equation using this theorem. The Mid- Point Theorem is also useful in the fields of calculus and algebra.

Step-by-step explanation:

Write the equation
y + 5 = 4(x + 2)
in slope intercept form
(y mx + b).

Answers

Answer:

y = 4x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b

Given

y + 5 = 4(x + 2) ← distribute the parenthesis

y + 5 = 4x + 8 ( subtract 5 from both sides )

y = 4x + 3 ← in slope- intercept form

2+2=????????????????????????????????????

Answers

It’s 4 if you have 2 cookies and your friend gives you 2 more that makes it 4

Answer:

The answer is 4

Step-by-step explanation:

1+1+1+1=4

what is the gcf of of -9y^2 + 6y

Answers

Answer:

3y

Step-by-step explanation:

First find the factors of the terms.  You need to then figure out how many factors match.

-9y² = -1 · 3 · 3 · y · y

6y = 2 · 3 · y

3y is the greatest common factor.

can anyone plz help?

Answers

Answer:

89.76 yd^2

Step-by-step explanation:

The area is given by

A = bh

A = 10.2 * 8.8

A =89.76 yd^2

Which of the following numbers are perfect squares? Choose all that apply. A 27 D 108 B 36 E 121 C 81 F 169

Answers

b, c, and e
6x6=36
9x9=81
11x11=108

algebra isn’t my best subject, please help

Answers

The Distributive property states that when we have the statement a(b + c), we can "distribute" the a by multiplying a times both terms that are inside the parenthses.

So in this problem, 2(5 + 7) can be simplified by distributing the

2 through both terms that are inside the set of parenthses.

So we have (2 · 5) + (2 · 7).

Answer:

Distributive Property

Step-by-step explanation:

You are distributing the 2 to the 5 and 7. which goes from 2(5+7) to 10+14.  

C. How do the processes you used for
parts A and B differ? How are they the same?

Answers

Answer:

Original Medicare comes in two parts. Medicare Part A covers hospital services, skilled nursing facility care, hospice, and some home health care. Medicare Part B covers medical services, including doctor visits, preventive screenings, certain vaccinations, lab tests, and durable medical equipment.

On a coordinate plane, a line goes through (negative 3, 2) and (2, negative 1). A point is at (3, 0). What is the equation of the line that is perpendicular to the given line and passes through the point (3, 0)? 3x + 5y = −9 3x + 5y = 9 5x − 3y = −15 5x − 3y = 15

Answers

Answer:

5x -3y = 15

Step-by-step explanation:

First find the slope of the line through ( -3,2) and (2,-1)

m = (y2-y1)/(x2-x1)

   =( -1-2)/(2--3)

   = -3/(2+3)

    = -3/5

We want a line that is perpendicular so the slopes will multiply to -1

m * -3/5 = -1

Multiply each side by -5/3

m * -3/5 * -5/3 = -1 *-5/3

m = 5/3

The slope of the perpendicular line is 5/3

We have a slope and a point

Using point slope form

y-y1 = m(x-x1)

y-0 = 5/3( x-3)

y = 5/3( x-3)

Distribute

y = 5/3x -5

Multiply each side by 3

3*y = 3(5/3x -5)

3y = 5x - 15

Subtract 5x from each side

-5x+3y = -15

Multiply each side by -1

5x -3y = 15

Answer:

D. 5x − 3y = 15

May I have brainliest please? :)

Find the volume for the following composite object.​

Answers

Answer:

[tex] Volume = 7440.16 ft^3 [/tex]

Step-by-step explanation:

Volume of the composite object = volume of cylinder - volume of rectangular prism

Volume of the composite object = πr²h - whl

where,

π = 3.14

r = 14 ft

h = 14 ft

w = 6 ft

l = 14 ft

[tex] Volume = (3.14*14^2*14) - (6*14*14) [/tex]

[tex] Volume = 8616.16 - 1176 [/tex]

[tex] Volume = 7440.16 ft^3 [/tex]

Which of the following characteristics of experiments are also characteristics of surveys? Check all that apply.

A. Data are gathered during the course of the study.
B. The study involves one or more treatment groups and a control group.
C. The study compares two or more treatments (possibly including no treatment")
D. Replication with different groups of subjects can improve the reliability of the study.
E. Statistical analysis is applied to the results of the study.

Answers

Answer: The best answers are :

A Data are gathered during the course of the study E. Statistical analysis is applied to the results of the studyD. Replication with different groups of subjects can improve the reliability of the study.

Step-by-step explanation:

I hope it helps :)

Answer:

a and c

Step-by-step explanation:

Tickets for a concert cost $2 for children, $3 for students, and $4 for adults. Ticket sales totaled $522 and 177 people attended the concert. Twice as many students as adults attended. Find how many of each type of ticket were sold. Assume that everyone who bought a ticket attended the concert.

Answers

Answer:

Children = 51

Adults = 42

Students= 84

Step-by-step explanation:

Children = $2

Students = $3

Adults = $4

Total sales = $522

Total people who attended = 177

Adults =a

Students = s= 2a

Children = c

c+s+a = 177 (1)

2c+3s+4a=522 (2)

Substitute s=2a into the equations

c + 2a + a = 177

c + 3a = 177 (3)

2c + 3(2a) + 4a = 522

2c + 6a + 4a = 522

2c + 10a = 522 (4)

c + 3a = 177 (3)

2c + 10a = 522 (4)

Multiply (3) by 2

2c + 6a = 354 (3b)

2c + 10a = 522

Subtract (3b) from (4)

10a - 6a = 522 - 354

4a = 168

Divide both sides by 4

a= 168/4

= 42

a= 42

s= 2a

= 2(42)

= 84

s= 84

Substitute the value of s and a into (1)

c+s+a = 177 (1)

c + 84 + 42 = 177

c + 126 = 177

c = 177 - 126

= 51

c=51

Children = 51

Adults = 42

Students= 84

ANSWER FAST ...............​

Answers

Answer:

The answer is

Step-by-step explanation:

First term 8. I am a 100% sure.

Hope this helps....

Have a nice day!!!!

|-12+3|= simply the expression

Answers

Answer:

|-12+3|=9

Step-by-step explanation:

Hello, -12+3=-9 and then we have to take the absolute value of -9, which is 9.

Thank you

Answer:

9

Step-by-step explanation:

|-12+3|

|-9|

9

f(x) = 3•2^x
h(x) = 2x - 7
h(f(2)) =

Answers

Answer:

17

Step-by-step explanation:

f(x) = 3•2^x

h(x) = 2x-7

f(2) = 3•2^2

= 3•4

= 12

h(f(2)) = 2(12) - 7

= 24 - 7

= 17

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________________ is the term given to how you say what you say. paralanguage pseudo-language verbal behavior double messages Suppose the test scores of students in a class are normally distributed with a mean of 86 and a standard deviation of 4. What is the z-score for a student that scored 76 on a test? A.4 .2.5 C.2.5 D.4 Quaker State Inc. offers a new employee a single-sum signing bonus at the date of employment. Alternatively, the employee can receive $8,600 at the date of employment plus $26,000 at the end of each of his first three years of service. Assuming the employee's time value of money is 8% annually, what lump sum at employment date would make him indifferent between the two options I had been told by Jack of the secret.(Simple / Compound / Complex / Items in a Series / Passive / Fragment) On arrival at a vehicle collision, you observe a small fire in the engine compartment. A bystander is attempting to smother the fire with a jacket as you approach with an A-B-C extinguisher from your ambulance. Which of the following is the best method of extinguishing the fire?a. Sweep the nozzle of the extinguisher left and right using short bursts until you are out of extinguishing agent.b. Aim at the base of the fire and use short bursts until the fire is out.c. Close the hood to contain the fire within the engine compartment.d. Aim the nozzle to the side of the fire and, with a sweeping motion, push the fire at its base f(x)= (1,2) (3, -4) (-5, -8) When the Chicago Police Department raised the minimum age for an applicant from 21 to 25, they did so because _____.the citizens of the City of Chicago demanded the change.younger individuals were not applying for jobs.older officers are more agile.they wanted a more mature police force. caractersticas del tringulo equiltero How many dots are there at t minutes? Solve the problems by your preferred method. Yoursolution should indicate how many dots will be in the pattern at 3 minutes, 100 minutes,and t minutes. Be sure to show how your solution relates to the picture and how youarrived at your solution. 2 which of the following is a perfect cubea) 400 -D. 3375C 8000 - The Master did not like people usingharsh words like 'brute' or 'beast' for thetiger. Why? He was the president for three years. In this sentence ( three, years or president )is a predicate ( Adjective or noun ) Help plzz i still have my F in english1. What are the benefits of summarizing a text?a. Summarizing takes the focus off of central ideas.b. Summarizing allows you to express your own opinions.c. Summarizing provides a lengthy, detailed description of the text.d.Summarizing can improve your comprehension.2. Which of the following should be included in a summary of a text?(1 point)a. the reader's conclusionsb. an interesting metaphorc. the central ideasd. the names of other texts on the same topic3. How is a summary different from a book review?(1 point)a. A book review includes ideas in the writer's own words, while a summary copies quotations directly from the text. b. A book review includes the opinions of others that have read the book, while a summary includes only the opinion of the person writing it.c. A book review may include the opinions of the person writing the review, while a summary should not include opinions.d. A book review includes the most important details in the book, while a summary includes only the main ideas.What is the best definition of a summary?choose all of the abovea. an essay presenting an opinion of a textb. a review of a range of opinions on a textc. a collection of important quotations from a textd. a brief, objective statement of the central ideas of a text In a working diode, the junction Diode During the current year, Orr Company incurred the following costs: Research and development services performed by Key Corp. for Orr $ 150,000 Design, construction, and testing of preproduction prototypes and models 200,000 Testing in search for new products or process alternatives 175,000 In its income statement for the current year, what amount should Orr report as research and development expense If y varies inversely as x, and y = 6 when x = 24, find x when y = 18 the historical method includes what steps ? Simplify: 7 - 3(2x - 5) - 4x 10 = 7 - m*It says solve & check solution. Can someone help asap describe a situation that could be modeled with the ration 4:1