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The complex numbers are solved using De Moivre's Theorem and then are matched with their respective solutions.

What is De Moivre's Theorem?

De Moivre's formula, also known as the theorem and identity of de Moivre, says that for any real number x and integer n, holds -

(cos x + i sin x)^n=cos nx + i sin nx

where i is the imaginary unit (i^2 = 1).

Also, [r(cos x + i sin x)]^n = r^n(cos nx + i sin nx) or [r cis x]^n = [r^n cis nx].

The first complex number is (1+i)^5.

Solve using De Moivre's formula -

(1+i)^5 = [√2{(1/√2)+(i/√2)}^5]

=(√2)^5[cos(π/4)+i sin(π/4)]^5

=(√2)^5[cos(5π/4)+i sin(5π/4)]

=(√2)^5[(-1/√2)-(i/√2)]

=4(-1-i)

=-4-4i

The second complex number is (-1+i)^6.

Solve using De Moivre's formula -

(-1+i)^6=(1-i)^6

=[√2{(1/√2)-(i/√2)}^6]

=(√2)^6[cos(-π/4)+i sin(-π/4)]^6

=(√2)^6[cos(-6π/4)+i sin(-6π/4)]

=8(0+1i)

=8i

The third complex number is 2[cos(20)+i sin(20)]^3.

Solve using De Moivre's formula -

2[cos(20)+i sin(20)]^3=2^3[cos(60)+i sin(60)]

=8[(1/2)+{(√3)i/2}]

=4+4√3i

The last complex number is 2[cos(π/4)+i sin(π/4)]^4.

Solve using De Moivre's formula -

2[cos(π/4)+i sin(π/4)]^4=2^4[cos(4π/4)+i sin(4π/4)]

=16[cos(π)+i sin(π)]

=16(-1+i(0)]

=-16

Therefore, the complex numbers are solved using the theorem.

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Answer:

the factors of 12 are 1, 2, 3, 4, 6, and 12. So the greatest common factor of 9 and 12 is 3. So you divide both sides by 3. So the simplest form of 9/12 is 34.

Step-by-step explanation:

hope his correct, .. sorry if not <33

can you mark branliest if right?

Answer:

3/4

Step-by-step explanation:

so you have 9/12, to ind the simplest form you would divide by 3 since you can multiply 3 to get these answers.

9/3=3

12/3=4

so the answer is 3/4

The length of jump by Pythagoras = 25 units

The length of jump by Newton = 29 units

The length of jump by Fermat = 20 units

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 length of the jump by Pythagoras be P

Let the length of the jump by Newton be N

Let the length of the jump by Fermat be F

Now , the equation will be

The total number of steps = 120 steps

The number of jumps by Pythagoras = 5 jumps

The number of steps overshoot by Pythagoras = 5 steps

So , P ( 5 ) - 5 = 120   be equation (1)

On simplifying the equation , we get

Adding 5 on both sides of the equation , we get

5P = 125

Divide by 5 on both sides of the equation , we get

P = 25 units

The number of jumps by Newton = 4 jumps

The number of steps fell short by Newton = 4 steps

So , N ( 4 ) + 4 = 120   be equation (2)

On simplifying the equation , we get

Subtracting 4 on both sides of the equation , we get

4N = 116

Divide by 4 on both sides of the equation , we get

N = 29 units

The number of jumps by Fermat = 6 jumps

So , F ( 6 ) = 120   be equation (2)

On simplifying the equation , we get

Divide by 6 on both sides of the equation , we get

F = 20 units

Therefore , the value of P , N and F are 25 , 29 and 20 units respectively

Hence , the length of each jump is 25 , 29 and 20 units

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Answer: 32x

Step-by-step explanation:

4x (3 + 5)

add 3 and

⇒ 4x (8)

⇒ 32x answer .

hope that helps...

The changes to the slope and to the intercept of the linear function after the transformation g(x) = f(x) + k, in which k = 2, are given as follows:

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients are given as follows:

The function f(x) in this problem is given as follows:

f(x) = -2x + 3.

Meaning that it has a slope of -2 and and intercept of 3.

The function g(x) is defined as follows:

g(x) = f(x) + k.

Since k = 2, we have that:

g(x) = f(x) + 2

g(x) = -2x + 3 + 2

g(x) = -2x + 5.

Hence the slope and the intercept are given as follows:

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Answer: the answer is the option

Employee B: gross pay $32,900, total job benefits $34,000

hope this helped you

Answer:

B

Step-by-step explanation:

Answer:

5  % per hour

Step-by-step explanation:

Pick two of the grid points the line seems to go through.  I'm using (0, 50) and (4, 70).

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\frac{70-50}{4-0}=\frac{20}{4}=5[/tex]

Answer:

150° : 30°

Step-by-step explanation:

total ratio

5 + 1 = 6

ratio 1

180 ÷ 6 = 30

ratio 5

30 × 5 = 150

Equation = P(1+r)^x, where P is the initial amount invested, r is the fixed interest rate, and x is the number of years.

It is important to note that the equation provided is the formula for compound interest. P is the initial principal, r is the annual interest rate, and x is the number of years the money is invested. The equation gives the total amount of money in the account after x years.

It should be also noted that the interest rate is given as a decimal and not a percentage.

For example, if the interest rate is 5%, then r = 0.05.

In order to use this equation, the value of P, r and x should be known

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The total number of cookies baker sold in all are 350 cookies.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, sugar cookies make up 38% of all sales for a local baker's cookie sales.

Let the total number of cookies be x.

Now, 38% of x=133

38/100 ×x=133

x=13300/38

x=350

Therefore, the total number of cookies baker sold in all are 350 cookies.

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what are u saying ????????/?

i can't read spanish

Answer:

[tex]7.8(sin23^o)[/tex]

Step-by-step explanation:

[tex]Sin23=\frac{opp}{hyp}[/tex]

[tex]Sin23=\frac{BC}{7.8}[/tex]

[tex]0.3907=\frac{BC}{7.8}[/tex]

[tex]BC=3.04746[/tex]

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

hope it helps...

have a great day!!

Answer:

If you want to find out how many print copies the book is selling, just click the Paperback or Hardcover edition of the book on Amazon, scroll down to Product Details on that page, and find the Amazon Best Sellers Rank for the print edition.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

if the denominator of a rational expression is zero then the expression will be undefined.

the numerator is the part of the rational expression that makes it zero.

solve the numerators in each to find values of x

1

[tex]\frac{x+6}{x-4}[/tex]

x + 6 = 0 ( subtract 6 from both sides )

x = - 6 ← value that makes expression equal to zero

2

[tex]\frac{(x+4)(x-2)}{x+6}[/tex]

(x + 4)(x - 2) = 0

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

x = - 4 and x = 2 make the expression equal to zero

3

[tex]\frac{2x+10}{3x-12}[/tex]

2x + 10 = 0 ( subtract 10 from both sides )

2x = - 10 ( divide both sides by 2 )

x = - 5 ← value that makes expression equal to zero

Answer:

1)  x = -6

2)  x = -4  and  x = 2

3)  x = -5

Step-by-step explanation:

A rational expression is undefined when the denominator equals zero.

A rational expression equals zero when the numerator equals zero.

Given rational expression:

[tex]\dfrac{x+6}{x-4}[/tex]

Set the numerator to zero and solve for x:

[tex]\implies x+6=0[/tex]

[tex]\implies x=-6[/tex]

Given rational expression:

[tex]\dfrac{(x+4)(x-2)}{x+6}[/tex]

Set the numerator to zero:

[tex]\implies (x+4)(x-2)=0[/tex]

Apply the zero-product property and solve for x:

[tex]\implies x+4=0 \implies x=-4[/tex]

[tex]\implies x-2=0 \implies x=2[/tex]

Given rational expression:

[tex]\dfrac{2x+10}{3x-12}[/tex]

Factor the numerator and denominator:

[tex]\dfrac{2(x+5)}{3(x-4)}[/tex]

Set the numerator to zero and solve for x:

[tex]\implies 2(x+5)=0[/tex]

[tex]\implies x+5=0[/tex]

[tex]\implies x=-5[/tex]

Answer:

D. 90

Step-by-step explanation:

If a triangle is inscribed inside of a circle, using the diameter as the hypotenuse, then the opposite angle of the hypotenuse is equal to 90 °

Because ΔABC is inscribed inside of the circle using the diameter it is a right triangle.

∠ABC is the angle opposite of the diameter therefore ∠ABC = 90°

Answer:

The fixed cost to insure jewellery is $0.602.

Step-by-step explanation:

We can use the information provided to set up a system of two equations in two variables, and then use the system to solve for the fixed cost of insuring the jewellery. Let x be the fixed cost and y be the percentage of the value of the jewellery. Then we can write the following two equations:

1000x + 1000y = 32 (1) (cost equation for insuring $1000 worth of jewellery)

3500x + 3500y = 44.5 (2) (cost equation for insuring $3500 worth of jewellery)

We can use either of these equation to solve for the fixed cost(x), to do that we can first solve for y from either of the equation, and then substitute it in other equation.

From equation (1)

y = (32 - 1000x) / 1000

then substitute this in equation (2)

3500x + 3500((32-1000x) / 1000) = 44.5

3500x + 32 - 3500x =44.5 - (1000x)

-20x = -12.05

x = 0.602 $

So, the fixed cost to insure jewellery is $0.602.

That means you have to pay $0.602 as a fixed cost, in addition to 0.01(y) as a percentage of the value of jewellery to insure it.

22 − ( ( ( 87 − 32 ) ÷ 5 ) × 2 )

Simplify each term.

22 − 22

Subtract  22  from  22 .

= 0

Answer: A

Step-by-step explanation:

Based on the graph, we know that it is negative if it is under the x-axis. It is also indicated by the negative labels.

A: correct

Looking at choice A, it says the interval is from -4<x<-2. This means we have to find x=-4 and x=-2. On the graph, that interval is below the x-axis, so it is negative.

B: incorrect

Looking at choice B, it says the interval is from -1<x<1. This means we have to find x=-1 and x=1. On the graph, that interval is above the x-axis, so it is positive, not negative.

C: incorrect

Looking at choice C, it says the interval is from 2<x<4. This means we have to find x=2 and x=4. On the graph, that interval is above the x-axis, so it is positive, not negative.

Therefore, A is the correct answer.

Answer:

the Annual percentage rate of shondra loan is 104.28%

Step-by-step explanation:

Given that

The borrowed amount is $200

The finance charge is $12

And, the term of the loan is 21 days

We need to find out the APR of the loan

so,

= (($12 ÷ $200) × 365) ÷ 21 × 100

= 104.28%

hence, the Annual percentage rate of shondra loan is 104.28%

Answer:

Combine like terms:

10y2 + 5ab

Step-by-step explanation:

Is your simplified algebraic expression.

Answer:

A. Triangular Prism

Step-by-step explanation:

Pyramids have a square base, so it's not that. and it is not rectangular, so it's not that either