Use the demoivres theorem

Use The Demoivres Theorem

Answers

Answer 1

The value of the given complex number is -1

De'moivres theorem

Given the polar form of a complex number expressed as:

[tex](cos\theta + isin\theta)^n\\[/tex]

This can also be expressed according to the de moivre's theorem as;

[tex]=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)[/tex]

Given the expression below;

[tex](cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1[/tex]

Hence the value of the given complex number is -1

Learn more on complex number here; https://brainly.com/question/10662770

#SPJ1


Related Questions

A system of three linear equations in three variables is inconsistent. how many solutions to the system exist? none one three infinitely many

Answers

None solutions to the system exist.

Given statement: A system of three linear equations in three variables is inconsistent.

Concept: If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables. (The “three variables” are the x, the y, and the z.) The numbers a, b, and c are called the coefficients of the equation.

We know that if a system has no solution, then it is known as inconsistent.

[If there are one, two, or an infinite number of solutions to the system, then it is called consistent.]

For more information about linear equations, visit https://brainly.com/question/14323743

#SPJ4

What is the slope of the line that passes through the points (-6, -6) and (-9,-5)? Write your answer in simplest form. What is the slope of the line that passes through the points ( -6 , -6 ) and ( -9 , -5)?​

Answers

Answer:

[tex]y=-\frac{1}{3}x -8[/tex]

Step-by-step explanation:

1) Write down the standard form of an equation of a line and the formula to find m.

[tex]y=mx+b[/tex]

[tex]m=\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

2) Find m using the formula then substitute it into [tex]y=mx+b[/tex].

[tex]m=\frac{-5 - (-6) }{-9 - (-6)}\\m=\frac{-5 +6 }{-9 +6}\\m=\frac{1}{-3} \\m=-\frac{1}{3}[/tex]

So, [tex]y=-\frac{1}{3}x +b[/tex].

3) Find b by substituting a pair of coordinates the line goes through.

[tex]-6=-\frac{1}{3}(-6) +b\\-6=2+b\\-6 - 2=b\\-8=b[/tex]

4) Substitute b into [tex]y=-\frac{1}{3}x +b[/tex] to get your final answer.

[tex]y=-\frac{1}{3}x -8[/tex]

find x and y

pls help

Answers

Answer X=14, Y=55
See diagram
To find X, I know the angles will equal 180
110 + 5x = 180
Subtract 110 from both sides to isolate X
5x = 70, solve for X, divide both sides by 5
X = 14
Do the same for Y
We know the triangle will equal 180
So (5x) is (5x14= 70) and the other angle is 40.
180-40-70 = 70 for the unknown angle in the triangle.
We know the angles in the Y part of the question will equal 180 so
70 + 2y = 180, subtract 70 from both sides to isolate Y
2y = 110, now solve for Y by dividing both sides by 2
Y = 55

Angles on straight line = 180

110 + 5x = 180 degrees

-110

5x. = 70

÷ 5

x. = 14

5 x 14 = 70

Angles in triangle = 180

70 + 40 = 110

So, the missing angle inside the triangle is 70

Now to find y, use angles on straight line = 180

2y + 70 = 180

- 70

2y = 110

÷2

y = 55 degrees

Hope this helps!

Which composition of transformations maps figure EFGH to figure E"F"G"H"?

a reflection across line k followed by a translation down
a translation down followed by a reflection across line k
a 180° rotation about point G followed by a translation to the right
a translation to the right followed by a 180° rotation about point G

Answers

The  composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.

What is the transformations rule that was used here?

A transformation is a rule that is used to manipulate the position of a point of geometric figure.

And from the figure, we can see that a translation is used, because of the movement of EFGH to figure E"F"G"H" which occurred in the same direction.

Hence,  composition of transformations maps figure EFGH to figure E"F"G"H" is Option A.a reflection across line k followed by a translation down.

Learn more about transformation from

https://brainly.com/question/3724552

#SPJ1

What's the sum Sn of the first n terms of this given sequence?

1, 1+2, 1+2+3, 1+2+3+4, ...
The kth term is 1+2+3+ ... +k =

(I also attached a picture of the question. Thanks!)

Answers

Answer: [tex]\frac{k(k+1)}{2}[/tex]

Step-by-step explanation:

This is a standard formula.

PLEASE HELP
a marine biologist tags 50 fish at lake ness and releases them. five days later, he captures 75 fish and finds that 3 of them are tagged. assuming the population of fish has remained constant over the five days and that this sample is an accurate representation of the portion of the fish in the lake that are tagged, how many fish are in the lake?

Answers

75 divided by 3 because for every 75 fish 3 are tagged 1,217 (rounded up from 1,216.6 repeating)

Let [tex]K[/tex] be a circle with centre [tex]O[/tex]. A second circle [tex]L[/tex] passes through [tex]O[/tex] and cuts [tex]K[/tex] at two other points [tex]A[/tex] and [tex]B[/tex]. Let [tex]P[/tex] be a point on arc [tex]AOB[/tex] and extend line segment [tex]BP[/tex] to intersect [tex]K[/tex] at a second point [tex]Q[/tex]. Prove that the bisector of angle [tex]APQ[/tex] passes through [tex]O[/tex].

Answers

The bisector of angle APQ passes through O and this is illustrated below.

How to illustrate the information?

From the information given, the center is O. and the circle passes through O and cuts at K.

In this case, it should be noted that the circles are equal according to the SAS test.

Here, AOB + APQ = 180° (Linear pair)

2AOB = 180

AOB = 90.

Therefore, the bisector of angle APQ passes through O.

Learn more about bisector on:

brainly.com/question/11006922

#SPJ1

Need answer & explanation! Please & thank you!

Answers

Answer: the correct is x=1,

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

x=1

Answer:

1

Step-by-step explanation:

you can plug it in and it gives you 3-1 which results in 2 as the question asks for

2. Marjorie wants to subdivide a rectangular plot of land measuring 600 m by 720 m
into equal square lots. What is the side length of the largest possible square lot
she can use? Show the prime factorization results to support your answer.

Answers

the largest length of the squares will be 120m.

What is the side length of the largest possible square lot she can use?

The largest possible length will be equal to the greatest common factor between the dimensions of the rectangular plot, so we need to find the GCF between 600 and 720.

If we decompose both numbers, we get:

600 = 2*2*2*3*5*5

720 = 2*2*2*2*3*3*5

Then the greatest common factor is: (2*2*2*3*5) = 120

So the largest length of the squares will be 120m.

If you want to learn more about greatest common factors:

https://brainly.com/question/219464

#SPJ1

can i have the x,y,z for this question? THanks!

Answers

Answer:

x=4, y=-2, p=14

Step-by-step explanation:

First simplify the LHS:

[tex]LHS = (16p^8)^\frac{3}{2} \times (216p^{-3})^{-\frac{2}{3}}[/tex]

[tex]= 64 p^{12} \times \frac{1}{36} p^{2}[/tex]

[tex]=\frac{16}{9}p^{14}[/tex]

[tex]=\frac{2^4}{3^2}p^14\\=2^43^{-2}p^{14}[/tex]

Hence x=4, y=2, p=14

y = x² + 3
y = x + 5

Answers

Answer:

x^2-x-2=0

Step-by-step explanation:

x^2+3=x+5

x^2-x-2=0

if the following data were linearized using logarithms, what would be the equation of the regression line? Round the slope and y-intercept of the regression line to three decimal places. x2,3,4,5,6 y73,77,85,101,133

A. log(y) =-1.706x + 0.064
B. log(y) =-0.064x + 1.706
C. log(y) = 1.706x + 0.064
D. log(y) = 0.064x + 1.706

Answers

The regression equation is (d) log(y) = 0.064x + 1.706

How to determine the regression equation?

The table of values is given as:

x   2   3   4   5   6

y   73  77  85  101  133

Calculate the logarithm of the y values.

So, we have:

x          2   3   4   5   6

log(y)   1.86  1.89  1.93  2  2.12

Next, we enter the above values in a regression calculator.

From the calculator, we have the following summary:

Sum of X = 20Sum of Y = 9.8Mean X = 4Mean Y = 1.96Sum of squares (SSX) = 10Sum of products (SP) = 0.63

The regression equation is then represented as:

log(y) = bx + a

Where:

b = SP/SSX = 0.64/10 = 0.064

a = MY - bMX = 1.96 - (0.064*4) = 1.706

So, we have:

log(y) = 0.064x + 1.706

Hence, the regression equation is (d) log(y) = 0.064x + 1.706

Read more about regression at:

brainly.com/question/17844286

#SPJ1

What is the value of "y" that satisfies the expression below?

1 y + 12 = 6 ( 1 y + 1 )

Round your answer to 2 decimal points (i.e. #.##)

Answers

Answer:

1.20

Step-by-step explanation:

1y + 12 = 6 (1y + 1)

1y + 12= 6y + 6

12 - 6 = 6y - 1y

6 = 5y

y = 6/5

y = 1.2

I don't what you meant by rounding to 2 decimal points so my answer is

1.20

Pls Help (question is in pic)

1. If the function holds true, in what year would the cost of mailing a first class letter reach 60 cents.

2. In 2007, the cost of mailing a first-class letter was 41 cents. Has the inflation rate stayed constant since 1991?

Answers

Based on the function given, the year when the cost of mailing a first class letter would reach 60 cents is 2007.

If the cost of mailing a first-class letter is 41 cents, then the inflation rate has not stayed constant.

What year does the cost reach 60 cents?

0.60 = 0.29 (1.046)^t

0.60 / 0.29 = (1.046)^t

log (2.07) = t x log (1.046)

t = 16 years

Added to 1991:

= 1991 + 16

= 2007

The cost of mailing a first-class ticket was 41 cents however which means that inflation was not constant.

Find out more on exponential growth models at https://brainly.com/question/13223520.

#SPJ1

Find the demand function for the marginal revenue function. Recall that if no items are​ sold, the revenue is 0.

R'(x) = 599 - 0.21sqrt(x)

What is the integral that is needed to solve the problem and the demand function?

Answers

The integral that is needed to solve the demand function is R(x) = 599x - 0.14[tex]x^{3/2}[/tex]

What is Demand Function?

A demand function describes the mathematical relationship between the quantity demanded and one or more determinants of the demand, as the price of the good or service, the price of complementary and substitute goods, disposable income, etc.

Here, given differential equation;

R'(x) = 599 - 0.21[tex]\sqrt{x}[/tex]

we can also write this as;

[tex]\frac{d}{dx}R(x) = 599 - 0.21\sqrt{x}[/tex]

[tex]d R(x) = (599 - 0.21\sqrt{x} ) dx[/tex]

On integrating both sides, we get

[tex]\int\ d R(x) = \int\ (599 - 0.21\sqrt{x} ) dx[/tex]

R(x) = [tex]599x - 0.21 X \frac{2}{3}x^{3/2}[/tex] + C

R(x) = 599x - 0.14[tex]x^{3/2}[/tex] + C       ...........(i)

Also given, at x = 0, R(x) = 0, Put these values in equation (i), we get

0 = 0 - 0 + C

C = 0

Put the value of C in equation (i), we get

R(x) = 599x - 0.14[tex]x^{3/2}[/tex]

Thus, the integral that is needed to solve the demand function is R(x) = 599x - 0.14[tex]x^{3/2}[/tex]

Learn more about Demand Function from:

https://brainly.com/question/20564722

#SPJ1

John missed 4 problems on a test but did 75% of them correctly. How many problems
were there in the test?

Answers

Answer:

16

Step-by-step explanation:

he missed 25%

if 4 = 25% then 16 questions total

4*4=16 and 25% * 4 = 100%

Answer: 16 problems

Step-by-step explanation:

First find out how many John got wrong. 100%-75%=25%. Then do cross multiplication: 4*100=25x; 400=25x. Divide 25 on both sides and... BOOM! you get 16 problems.

Pls help! Geometry
Find the area

Answers

It’s been a while but I got 364.14
i believe the correct answer should be 364.14 maybe

Thomas traveled north 24 miles and then 15 miles west. Find the shortest distance between the start and end points. 15 miles O 24 miles 28.3 miles 32.8 miles Thomas traveled north 24 miles and then 15 miles west . Find the shortest distance between the start and end points . 15 miles O 24 miles 28.3 miles 32.8 miles​

Answers

The distance between the start and end points is 28.3 miles.

How to find the distance?

Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_2 -y_1)^2}[/tex]

Here the initial point is (0mi, 0mi).

If we define the north as positive y-axis and east as the positive x-axis, after that Thomas travels 24 miles north and 15 miles west his new position is:

(-15mi, 24mi).

The distance is then:

[tex]d = \sqrt{(-15mi - 0mi)^2 + (24mi - 0mi)^2} = 28.3mi[/tex]

If you want to learn more about distances you can read:

https://brainly.com/question/7243416

#SPJ1

HELP ME! what is the measure of the supplement of each angle? 165°

Answers

Answer:

15

Step-by-step explanation:

Supplementary angles add to 180 degrees

Let the supplement be x

x+165 = 180

x +165-165= 180-165

x = 15

The supplement is 15

Answer:

Hello! The answer is 15°.

Step-by-step explanation:

Supplementary angles add up to 180°.

To find the measure of each angle, we can now set up an equation because we have the total that supplementary angles add up to:

x + 165 = 180

Now, we can subtract 165 from both sides to get x by itself:

x + 165 = 180

    -165  -165

This leaves us with:

x = 15

Determine if the given ordered triple is a solution of the system.

(4, -5, -4)
4x + 2y + z = 2
5x - 4y - z = 44
3x + y + 4z = -9

Answers

Answer:

It is.

Step-by-step explanation:

(x, y, z) => (4, -5, -4)

substitute 4 in x, -5 in y & -4 in z for all the equations in the system.

4x + 2y + z = 2

4(4) + 2(-5) - 4 = 2

2 = 2

5x - 4y - z = 44

5(4) - 4(-5) - (-4) = 44

44 = 44

3x + y + 4z = -9

3(4) + (-5) + 4(-4) = -9

-9 = -9

All equations therefore agree with the ordered triple.

The total interest on a discounted loan is $80. If James received $880 into his bank account on drawdown, and the loan lasts for 6 months, what is the (simple) interest rate? Give your answer as a percentage to the nearest tenth of a percent.

Answers

With the use of formula, the interest rate is 18.2%

How can Simple Interest be Calculated ?

The Interest is the product of the principal, time and the rate in percentage. That is, I = PTR / 100

Where

P is the Principal = $880T is the time = 6 months = 0.5 yearR is the rate = ?I is the interest = $80

Substitute all the parameters into the formula

80 = (880 x 0.5R)/100

cross multiply

8000 = 440R

R = 8000/440

R = 18.2%

Therefore,  the (simple) interest rate is 18.2%

Learn more about Simple Interest here: https://brainly.com/question/2294792

#SPJ1

Select the properties of a square? please answer, I'm desperate ​

Answers

Answer:

all are the properties of square

Step-by-step explanation:

all are correct

Tony makes a table to use as a quick reference guide:
Cookies baked (y) is a function of number of batches (x).

Use the table tool to answer the question.

How many cookies will Tony have if he bakes 10 batches more than the maximum number of batches in the table?

Enter the correct answer. ​

Answers

Tony will have 486 cookies if he bakes 10 batches more.

Take two points from table: (8, 234), (9, 252)

Find slope:

[tex]slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow slope \ (m) : \dfrac{252-234}{9-8} = 18[/tex]

This determines that one batch of cookies has 18 cookies.

So, if he bakes 10 more batches:

(10 × 18) = 180 cookies

Total cookies he then will have:

306 cookies + 180 cookies = 486 cookies.

What is the equation of the line AB, if it passes through (-4,0), and is parallel to the line
-x - 4y = 1?

Answers

Rewriting the equation of the given line in slope-intercept form,

[tex]-x-4y=1\\\\-4y=x+1\\\\4y=-x-1\\\\y=-\frac{1}{4}x-\frac{1}{4}[/tex]

From this, we know the slope of the given line is -1/4.

Since parallel lines have the same slope, we know the line whose equation we want to find has a slope of -1/4.

Substituting into point-slope form,

[tex]y=-\frac{1}{4}(x+4)\\\\\boxed{y=-\frac{1}{4}x-1}[/tex]

Pls help! Geometry
What is the total cost of material for bunny costumes?

Answers

Answer: $201.81

Step-by-step explanation:

The total amount of faux fur required is [tex]6(3.1)=18.6[/tex] square yards.

Multiplying this by $10.85 per square yard, we get the total cost is [tex](18.6)(10.85)=\$201.81[/tex]

The diameter of a sphere is
a chord that passes through the center of the sphere.
a fixed point equidistant from all points on the surface of the sphere.
a line segment from the center point to a point on the sphere.
a three-dimensional circle in which all points are equidistant from a fixed point.

Answers

The diameter of a sphere is a chord that passes through the centre of the sphere.

We need to complete the given statement.

What is the diameter of the sphere?

The diameter of a sphere is the maximum distance between two antipodal points on the surface of the sphere. If is the radius of a circle or sphere, then. The ratio of the circumference of a circle or great circle of a sphere to the diameter.

A chord of a sphere is a segment whose endpoints are on the sphere. A diameter is a chord that contains the centre.

Therefore, the diameter of a sphere is a chord that passes through the centre of the sphere.

To learn more about the sphere visit:

https://brainly.com/question/12063484.

#SPJ1

which graph shows the system of inequalities y<-1/3x+1 and y≤2x-3

Answers

The graph of the system of inequalities can be seen below.

Which graph shows the solution for the system?

Here we have the inequalities:

y < -(1/3)*x + 1

y ≤2x-3

To graph the first inequality, we need to graph the line -(1/3)*x + 1 with a dashed line (because the symbol < was used) and shade the region below that line.

For the second inequality we need to graph the line 2x-3 with a solid line this time, and again, shade the region below the line.

The graph of the system is shown in the image below.

If you want to learn more about inequalities:

https://brainly.com/question/18881247

#SPJ1

Write a proportion for the statement.
40 is to 10 as 32 is to 8.

Answers

Hi! ⋇

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

  All proportions have this form:

  [tex]\sf{\dfrac{a}{b}=\dfrac{c}{d}}[/tex], Where [tex]\sf{\dfrac{a}{b}}[/tex] is equal to [tex]\sf{\dfrac{c}{d}}[/tex].

 If [tex]\sf{\dfrac{a}{b}\neq\dfrac{c}{d}}[/tex], it's not a proportion.

_________________________

  Here we have two pairs of numbers:

40,10 and 32,8.

Written As a proportion, they look like :

[tex]\sf{\dfrac{40}{10}=\dfrac{32}{8}}[/tex]

Hope this made sense to you :)

[tex]\it{Calligrxphy}[/tex]

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

3 red balls, 4 white balls, and 1 green ball are in a bag. Balls are drawn without replacement. Find the probability that the red balls can be drawn before the green ball is drawn.

Answers

The probability that the red balls can be drawn before the green ball is drawn is 3/8.

What is Probability?

The probability is the measure of the likelihood of an event to happen.

Given:

red balls= 3

white balls = 4

green balls = 1

So, Probability of red balls

=3/8

Probability of green balls

=1/7

Learn more about probability here:

https://brainly.com/question/14546377

#SPJ1

please help! :(
Kathy distributes jelly beans among her friends. Alia gets 4^2 fewer jelly beans than Kelly, who gets 3^3 jelly beans. How many jelly beans does Alia get?

a. 4^2 - 3^3
b. 3^3 + 4^2
c. 4 - 3^3
d. 3^3 - 4^2
e. 3^2 - 4^3

Answers

Answer:

d.

Step-by-step explanation:

k gets 3^3

a gets 4^2

subtract 3^3-4^2=d.

Other Questions
Naomi's good friend tells Naomi that she has an opportunity for her to make some extra money. Her friend asks Naomi for $100 and tells her she will get back $250 by the end of the week. Naomi doesn't ask for specific details but gets the impression that the opportunity is not on the "up and up." Reflection Questions: Does Naomi have a responsibility to make sure she understands the specific details of the opportunity before deciding whether to lend her money? Explain why or why not. Should Naomi lend her friend $100 with the promised return of $250? Explain why or why not. Explain how Naomi's decision in Question 2 demonstrates a pre-conventional, conventional, or post-conventional level of moral reasoning in complete sentences. According to the table, which ordered pair is a local maximum of the function, f(x)?(0, 64)(3, 35)(5, 189)(2, 0) Solve the inequality. Which statement best describes the purpose of the conclusion paragraph in aliterary analysis essay?A. It synthesizes evidence.OB. It states the claim.C. It addresses counterclaims.D. It summarizes the evidence. Ten six graders will each eat 1/4 of a pizza. How many whole pizza pies need to beordered for the ten students? Show your work What is 200in simplest form? What are the Result of reaction between , Isoquinoline and alkali KMNO4 ? Refer to Table 24-1. If Year 1 is the base year, then the inflation rate in Year 2 wasa. 2.10 percent.b. 1.40 percent.c. 3.90 percent.d. 1.40 percent. The table shows the percentage of carbon dioxide in the Earths atmosphere in the years 1800 and 2013. Calculate the difference in the mass of carbon dioxide in 500 kg of air in 2013 compared to 1800. Select the correct answer. MATH: FINDING HALF LIFE PT 1 Can someone help me out with these questions ? which of the following is a fifth root of the given complex number? NEED THIS ASAP.What is the fate of the speaker in The Wanderer?He can not be forgiven by his familyHe must endure a perilous journeyHe is forgotten by his lord and comrades What is the value of the Pearson coefficient of skewness for a distribution with a mean of 17, a median of 12, and a standard deviation of 6 Write 3 paragraphs telling the readers what impact new technology during the gilded age a2 6) and (a2 + 4) are the factors of While in the short run an economic profit is more likely in an unregulated monopoly, ___________ may group competing resources and create a new power base to challenge the existing monopoly. explain how principles of computational thinking skills are applied in finding solutions that can be interpreted into software applications Never use a ______________ extinguisher in a confined space, as its discharge will replace the oxygen in the air and make it difficult to breathe. In addition, after discharge, the extinguishers nozzle will become extremely cold and may damage your skin. what are conflicting attitudes towards the role of money in this family? what does money mean to each of the main characters