Use DeMoivre’s Theorem to find (3cis(pi/6))^3.
a.) (27sqrt3)/2 +27/2 i
b.) (9sqrt3)/2 +9/2 i
c.) 27i
d.) 9i

Answers

Answer 1

Answer:

C. 27i

Step-by-step explanation:

Given the complex number in polar coordinate expressed as

z = r(cos∅+isin∅)

zⁿ =  {r(cos∅+isin∅)}ⁿ

According to DeMoivre’s Theorem;

zⁿ =  rⁿ(cosn∅+isinn∅)

Given the complex number;

(3cis(pi/6))^3

= {3(cosπ/6 + isinπ/6)}^3

Using  DeMoivre’s Theorem;

= 3³(cos3π/6 + isin3π/6)

=  3³(cosπ/2 + isinπ/2)

= 3³(0 + i(1))

= 27i

The right answer is 27i


Related Questions

A triangle has angles that measure 59°, 48°, and 73°. What kind of triangle is it?

Answers

Answer: it is an isosceles triangle

Step-by-step explanation:

all three angles are lower than 90 degrees. if the angles were all higher than 90 degrees the triangle would be considered obtuse.  even though all the angles are lower than 90 degrees, it would also be considered acute.

need answer asap!!!!!!!!!!!

Answers

Answer:

126 degrees

Step-by-step explanation:

A straight line makes a 180 degree angle. Since we know one side is 54, just subtract 54 from 180.

What is the solution to the equation ^3sqrtX+4+ ^3sqrt2X+8=0?
x = –12
x = –4
x = 4
x = 12

Answers

Answer:

Cover 2

Step-by-step explanation:

Answer:

Uhh x is like -4 bruh

Step-by-step explanation:

So b on edge ye

Find the measure of the third angle of a triangle if the measures of the other two angles are given. 31.8 and 89.8

Answers

Answer:

58.4 Degrees

Step-by-step explanation:

Look at the attachment

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The measure of the third angle of a triangle is 58.4°.

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The sum of all the angle of the traingle is always 180°.

31.8° + 89.8° + x = 180°

x = 58.4°

Hence, the measure of the third angle of a triangle is 58.4°.

Learn more about Triangle:

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I will give you all five stars ⭐⭐⭐⭐⭐

Answers

Answer:

B

Step-by-step explanation:

Seeing as the change is consistent within the vertices, this would be correct.



Find the area of the pentagon.
A) 107 inches2
B) 116 inches2
C) 150 inches2
D) 182 inches2

Find the area of the pentagon.
A) 107 inches2
B) 116 inches2
C) 150 inches2
D) 182 inches2

Answers

Answer:

A

Step-by-step explanation:

Answer:

A) 107 inches2

Step-by-step explanation:

4*16= 64

64/2 = 32

9+16 = 25

25/2 = 12.50

12.50*6 = 75  

32 + 75 = 107

Got it right in USA TESTING

Find the value of x.

Answers

Answer:

x=51

Step-by-step explanation:

Formula:  35+16=x

Step 1: Simplify both sides of the equation.

35+16=x

(35+16)=x(Combine Like Terms)

51=x

51=x

Step 2: Flip the equation.

x=51

Hope this helps.

Hattie accepted a job as a makeup artist after being offered a $550 signing
bonus. If she makes $32 an hour, which equation models Hattie's total pay y,
in dollars, as it relates to the number of hours x that she works?

Answers

The equation would be y=32x+550. 32 an hour is represented by 32x since she earned 32 an hour. 550 is the extra amount she is getting paid.

I hope this helps.

Answer:

y=32x+550

Step-by-step explanation:

Question 1 (1 point)
A box of eleven chocolates contains: four Milk Chocolates, four Dark Chocolates, and three
White Chocolates. Find the probability you randomly select a chocolate that is a Milk
Chocolate or a Dark Chocolate.
Find P(Milk Chocolate U Dark Chocolate)
72.7%
0 66.7%
33.3%
15.4%

Answers

The correct answer would be 72.7%

Which fraction is equivalent to 15/30
A 3/4
B 2/4
C 3/5
D 5/6

Answers

Answer:

2/4

Step-by-step explanation:

2/4ths because 15/30 is 1/2 which isn’t on here but 2/4th is equal to 2/4

HURRY STRANGERS PLEASE I REALLY NEED THIS!!! A paper manufacturer is evaluating their packing procedures. Currently, they package twelve reams of paper in a box—in three stacks of four reams. However, their company has been getting complaints from the retail stores that the box is too large and heavy for the average consumer to carry by their self. So, they have decided to reduce the weight of each box by ten pounds. You have been asked to explore the different packing options based on the new weight condition and present your recommendation to the CEO of the paper company.


Identify three unique ways to package the paper given the new weight condition. Include both the dimensions of the new boxes, as well as a verbal description of how the reams will be packaged. You may include sketches if you wish.

Answers

Answer:

Step-by-step explanation:

Base on my own understanding what should be done is that three stacks will not work, because it wont be a symmetric arrangement and also one will be left out. So, two stacks of five each would be better and easy to carry. But the stacks should be arranged in such a manner that the lengths will be parallel to each other and not in-line which would increase the length making it comparatively very long. its easier to hold a (2*8.5,11,2*5=17,11,17) compact box, because it will be easy to carry a long and not heavy.

This recipe will serve 12 pancakes.
Find out how much of each ingredient you would need for 24 pancakes.
Find out how much of each ingredient you would need for 6 pancakes.
Ingredient
12 pancakes
24 pancakes
6 pancakes
4
Eggs
11 tsp
Flour
tsp
Baking Powder

Answers

24 pancakes 8 eggs 22 tsp of flour and 2 tsp of baking powder

6 pancakes 2 eggs 5 1/2 tsp of flour and 1/2 tsp of baking powder

Help ASAP please ! Explain too if you can

Answers

Answer:

B

Step-by-step explanation:

180-118=42 so angle c=42

add 42 +76 =138

in a triangle all degrees ad up to 180 so

subtract 138 from 180=42

Answer:

B) 42 degrees

Step-by-step explanation:

If we're looking for the measure of angle E, we need to know the measures of angles D and C too. (Otherwise we just have nothing to work with.)

So they already give us angle D's measurement, which is 76; we just have to find the smaller angle at C and then solve for E. If this doesn't make sense, just look at C; there's a big angle (118) and a small one that we don't know. We have to find the small one.

Well at C there's just a straight line, so we can assume that the big angle and the small angle add up to 180 degrees, because straight angles are always 180 degrees.

Now to get the small angle, we can take 118 away from 180 to get 62, which will be the measure of the smaller angle. (Comment if you don't know why I did this.)

Now that we know two out of three measures in the triangle, we can find the measure of angle E. All triangles' angles add up to 180 degrees, so we can take away 76 (measure of D) and 62 (measure of small C) from 180 to get the measure of E: 180 - 76 - 62 = 42

So the measure of angle E is 42.

Use the Remainder Theorem to find the remainder for (2x^3- 3x^2+x)/(x-1) and state whether or not the binomial is a factor of the

polynomial.

Answers

remainder = 0
I’m so sorry if it’s incorrect :(

As 2x³ - 3x² + x is completely divisible by x - 1 it is a factor of the polynomial.

What is a factor of a polynomial?

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given a polynomial 2x³ - 3x² + x which is being divided by x - 1.

Now, If 2x³ - 3x² + x is divisible by x - 1 then x = 1 is a root of the polynomial

2x³ - 3x² + x.

Therefore,

2(1)³ - 3(1)² + 1 = 0

2 - 3 + 1 = 0.

3 - 3 = 0.

0 = 0.

So, The binomial x - 1 is a factor of the polynomial.

learn more about the remainder theorem here :

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what is s10 for 1 + 2 + 4 + 8+...

256
511
1023
2047

Answers

Answer:

1023

Step-by-step explanation:

[tex] S_n = \dfrac{a(1 - r^n)}{1 - r} [/tex]

a = first term

r = common ratio

n = number of terms

Here we have

a = 1

r = 2

n = 10

[tex] S_{10} = \dfrac{1(1 - 2^{10})}{1 - 2} [/tex]

[tex] S_{10} = \dfrac{1 - 1024}{-1} [/tex]

[tex] S_{10} = \dfrac{-1023}{-1} [/tex]

[tex] S_{10} = 1023 [/tex]

Of course, since 10 is not such a large number of terms, you can simply do this:

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1023


A painter pays $15 per can of paint. How many cans of paint can she buy with $1052

Answers

Answer:

70 cans

Step-by-step explanation:

1052/15=70.1333333

but you have to round down to 70

ANSWER: 70

EXPLANATION:

find x and y i will give brainliest

Answers

Answer: N= 135, M=45.

Step-by-step explanation:The formula to find the degree inside of a shape is: (n-2)180. This is an octagon, so it has 8 sides, plug this in for n.

8-2 * 180

1080                              divide by 8 to get the value of n

n=135

The formula for an angle outside of the shape is:

360/n   n is still eight, so plug this in for n

360/8

m=45

Answer:

n = 135 degrees ( ° ) ,

m = 45 degrees ( ° )

Step-by-step explanation:

* Sorry I didn't answer this before *

1. In this figure we can see that this visual is a representation of an octagon, provided it's 8 sides.

2. Knowing this, let us split this figure into triangle 180 degrees each ⇒ compute the total interior angles in degrees.

3. If you were to draw lines from one vertex to any other non-adjacent vertices, it would be that 6 triangles are formed.

4. One triangle ⇒ 180 degrees ( ° ) so that this octagon ⇒ 180° * number of triangles, or ⇒ 180 * 6 = 1080°

5. Knowing that this shape is a regular polygon, all angles are congruent such that if x represents one interior angle ⇒ 8x = 1080, ⇒ x = 135°. As n acts as one of the interior angles in this figure ⇒ n = 135 degrees ( ° )

6. Now through supplementary angles, the interior angle adjacent to angle m would form a linear pair, adding to 180°.

7. This would mean that m + interior angle = 180, and as all interior angles were found to be 135 degrees ⇒ m + 132 = 180 ⇒ m = 45 degrees ( ° )

pls help will mark as brainliest

Answers

Answer:

1. Onesimus is the box 1

2. Gauls is box 8

3. Tarsus is box 3

4. Damascus is box 6

5. Ephesus is box 9

6. Colossae is box 12

7. Thessolonica is box 4

8. Ananias is box 2

9. Philippians is box 7

10. Tychicus is box 10

11. Phoebe is box 5

12. Epaphrase is box 11

Step-by-step explanation:

Hope this helps.

What number is the opposite of 98?

Answers

Answer:

-98

Step-by-step explanation:

hope this is right

Answer:

-98

Step-by-step explanation:

a negative number is the opposite of a positive number

what time will it be 2 1/2 hours later after 5:55pm

Answers

Answer:

8:25

Step-by-step explanation:

pls help will mark as brainliest

Answers

Answer:

1/3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

It would have to be 3, because it says that 1/3 is wrong.

Can someone help me with this? ;^;

Answers

Answer:

The mode would be 10

Step-by-step explanation:

Because it is there more than the others

hope this helps! =D

Answer:

10

Step-by-step explanation:

many organize a classroom party. there are 20 of cold drinks at the party, 13 of which contain diet Pepsi, what is the probability that randomly selected drink will be a diet Pepsi? answer key

Answers

Answer:

so its either 13/20

Step-by-step explanation:

if you get this wrong sorry:(

The answer is 13/20

Explanation:
20 is the denominator because it is how many drinks there are in total. 13 is the numerator because that’s how many are Diet Pepsi’s and you cannot simplify this. That’s why the answer in 13/20.

P.S whenever you can simplify this you should :)

What is the interquartile range (IQR) of this data set?
3, 7, 8, 11, 13, 15, 16

Answers

25th Percentile: 7

50th Percentile: 11

75th Percentile: 15

     Answer:

Interquartile Range: 8

The IQR is 8 I believe

Two different sports teams are doing fundraising to be able to afford their uniforms. The softball team needs to raise $318.12 between the twelve girls on the team. The hockey team needs to raise $391.92 between the 24 boys on the team. If each player raises the same amount of money, does each softball player or hockey player need to raise more? How can estimation help you solve?

Answers

Answer: A softball player will need to raise more.

Step-by-step explanation:

The softball team needs to raise $318.12 among the twelve girls on the team. Each softball player needs to raise:

$318.12 ÷ 12 = $26.51

The hockey team needs to raise $391.92 among the 24 boys on the team. Each hockey player will raise:

$391.92 ÷ 24 = $16.33

A softball player will raise $26.51 while a hockey player will raise $16.33. Therefore, a softball player will need to raise more.

What factors do 6 and 12 have in common?

Answers

Answer:

6x^2 im pretty sure thats whats its asking for

Step-by-step explanation:

Can someone please help me with this?

Answers

i’m doing the first one.

the filled in circle goes to the 8 and put an arrow facing the right.

inequality-

x ≥ 8

Which sentence is true?
A. - 3 > - 7
B. - 2 < -9
C. 4 < -1
D. - 5 > 0

Answers

Answer:

A

Step-by-step explanation:

I believe A. is true for the question

2. The size of a conC. 3 times the size of a cylinder is:
A. 1/3 the size of a cylinder.
B. 2/3 the size of a cylinder.
C. 3 times the size of a cylinder.
D. the same as the size of a cylinder.

Answers

Answer:

The answer is A.

Step-by-step explanation:

What number should both sides of the following equation be multiplied by to solve for x?

x/7.25 = 4

4
7.25
7
29

Answers

Answer:

[tex] \frac{x}{7.25} = 4 \\ x = 4 \times 7.25 \\ x = 29[/tex]

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