What is 56(cos(33°) + i sin(33°)) ÷ 7(cos(11°) + i sin(11°))?
8(cos(3°) + i sin(3°))
49(cos(3°) + i sin(3°))
8(cos(22°) + i sin(22°))
49(cos(22°) + i sin(22°))

Answers

Answer 1

C. <3

pls give brainlyist

Answer 2

[tex]56(cos(33^{\circ}) + i sin(33^{\circ})) \div 7(cos(11^{\circ}) + i sin(11^{\circ}))\\\\=8(cos(22^{\circ}) + i~ sin(22^{\circ}))[/tex]

What is complex number?

"The number of the form a + ib, where a, b are real numbers and [tex]i=\sqrt{-1}[/tex]"

What is De Moivre's theorem?

"This theorem gives a formula for computing powers of complex numbers.

[tex](r(cos\theta+i~sin\theta))^n=r^n~(cos(n\theta)+i~sin(n\theta))[/tex] "

For given question,

We need to divide two complex numbers.

[tex]56(cos(33^{\circ}) + i sin(33^{\circ})) \div 7(cos(11^{\circ}) + i sin(11^{\circ}))[/tex]

Consider,

[tex]56(cos(33^{\circ}) + i~ sin(33^{\circ})) \div 7(cos(11^{\circ}) + i ~sin(11^{\circ}))\\\\=8[(cos(33^{\circ}) + i~ sin(33^{\circ})) \div (cos(11^{\circ}) + i ~sin(11^{\circ}))][/tex]                 ...........(i)

Consider the first complex number.

[tex](cos(33^{\circ}) + i sin(33^{\circ}))[/tex]

We can write this complex number as,

[tex]cos(3(11^{\circ}) )+ i sin(3(11^{\circ}))[/tex]

By De Moivre's theorem,

[tex]cos(3(11^{\circ}) )+ i~ sin(3(11^{\circ}))\\\\=(cos(11^{\circ})+ i~ sin(11^{\circ}))^3[/tex]

Substitute this value in (i),

[tex]56(cos(33^{\circ}) + i~ sin(33^{\circ})) \div 7(cos(11^{\circ}) + i ~sin(11^{\circ}))\\\\=8[(cos(33^{\circ}) + i~ sin(33^{\circ})) \div (cos(11^{\circ}) + i ~sin(11^{\circ}))]\\\\=8[(cos(11^{\circ}) + i~ sin(11^{\circ}))^3 \div 7(cos(11^{\circ}) + i~ sin(11^{\circ}))]\\\\=8[(cos(11^{\circ}) + i~ sin(11^{\circ}))^2]\\\\=8[(cos(2\times 11^{\circ}) + i~ sin(2\times 11^{\circ}))]~~~~~~~~~.............(De~Moivre's~theorem )\\\\=8(cos(22^{\circ}) + i~ sin(22^{\circ}))[/tex]

Therefore, [tex]56(cos(33^{\circ}) + i sin(33^{\circ})) \div 7(cos(11^{\circ}) + i sin(11^{\circ}))[/tex] is [tex]8(cos(22^{\circ}) + i~ sin(22^{\circ}))[/tex]

Learn more about the De Moivre's theorem here:

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Related Questions

6a-2a=2a(3-1) - what property is this

Answers

Answer:

Distributive and associative.

Step-by-step explanation:

The equation involves distributing, and rearranging the order, so the properties are distributive and associative.

Hope this helps, and have a great day!! C:

Look at the following numbers:
-7, 0, 7, 14
Which pair of numbers has a sum of 0?
O 0,7
O-7,7
07, 14
O-7, 14

Answers

The answer is B: -7, 7
Yeahhhhb the answer is b

In George’s classroom, there are 6 girls for every 2 boys. What is the ratio of boys to the total number of students?

Answers

Answer:

6;2

Step-by-step explanation:

Answer:

1:3

Step-by-step explanation:

Help I’m giving all my points for this question and brain will be given

Answers

Answer:

55,000

Step-by-step explanation:

Look at 40 on the x-axis and the y-axis. The line is inbetween 50 and 60 so the best answer would be 55,000

How long will it take a car to go 100 miles
traveling at a speed of 25 miles per hour

Answers

25 times 100 = 2,500

what type of angles are these TWO angles?

answer choices:

adjacent angles
. linear pair
. vertical angles
.complementary angles

Answers

Answer:

linear pair.

Step-by-step explanation:

i know this because the angles are slightly. tilted unlike complementary and vertical angles.

hope this helps.

A map has a scale of 2 inches : 25 miles. Gabriel uses the map to find the
distance from the zoo to his house. The distance on the map is 5 inches. If
Gabriel bikes at a rate of 12.5 miles per hour, how long will it take him to get to
the zoo?

Answers

2 hours. It's extremely simple this is elementary grade, he needs to travel 25 miles and he's going 12.5 miles an hour, 12.5 x 2 = 25 So in 2 hours he reaches his destination.

The time it will take will be 5 hours.

What is ratio?

"The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related. For example, the ratio of boys to girls in a class is 12: 15, whereas, the part-to-whole ratio denotes the relationship between a specific group to a whole. For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books."

The speed of the bike = 12.5 miles/hour

So, the distance will be = [tex]25/2 * 5 = 125/2[/tex]

Time taken = [tex]125/2 * 1/12.5[/tex]

= 5 hours

Hence, the time taken to get to the zoo = 5 hours

To know more about ratio here

https://brainly.com/question/13419413

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What is angle MNT? Help

Answers

Answer: acute

Step-by-step explanation: it is less than 90 degrees so it is less the right angle

120 degrees.

Angle MNT is equal to its opposite angle, (I cant tell you the angle as one of the points is not showing, it uses T and Q)

Remember, all triangles have angles that when added together, equal 180 degrees.

So, add 35 and 25, which is 60.

Now subtract 60 from 180, 120.

Have a great day!

I need help I don't understand it ​

Answers

The second one is non linear because the values for y and x are not directly proportional

It would be linear if it was 0 instead of -1.5


3) Game stop is having a Black Friday sale. Every item in the store is
advertised as 2/5 off the original price. Cristiano decides to use a coupon
that will take an additional 1/10 off the sale price. If a game is originally
$65. how much does Cristiano pay for the game?

Answers

Answer:

$32.50

Step-by-step explanation:

2/5 = 40%

1/10 = 10%

65/2 = 32.5

It’s not A 0.17 !!!!!

Answers

I’d say probably .44

Answer:

0.25

Step-by-step explanation:

MY
LAST
QUESTION (NEED HELP ASAP) PLEASE!!!!

Answers

Answer:

The answer is A

Step-by-step explanation:

Find the area of this trapezoid

Answers

Answer:

sol: here

side a=4cm

side b=6cm

vertical length=6 cm

1/2×(4+6)×6

30 cm^2

Answer:

ok so i think its 30 MARK AS BRANLIEST BCUZ I SAVED YOU

Step-by-step explanation:

area is 1/2x6x(4+6)

then it is 3(10)

=30

What is the domain of the following function

Answers

Answer:

3,5,-3,9

Step-by-step explanation:

Domain is x(left circle) while range is right circle(y), meaning the answer is 3, 5, -3, 9.

OMG I NEED HELP!!!!!

Answers

Answer:

6

Step-by-step explanation:

9/3=3, so if you divide 18/3, you get 6.

Hope this helps you out!! Have a wonderful day :3

Answer:

6

Step-by-step explanation:

This type of problem is a lot easier when you break it down a bit.

First, we know that 9:18 is equal to 1:2 (this is just simplifying by dividing by 9)

So, what's 2*3? 6

Alternatively, you can reason that 9/3 = 3 and 18/3=6

Hope this helps!

Of the students in Jill's grade, 41 students have a pet and the other 7 students do not. What is the ratio of the number of students who do not have a pet to the total number of students?

Answers

Answer:

The answer is 7 : 48.

Step-by-step explanation:

First, you can to calculate how many students are there in Jill's grade by adding the number of students who have pet with the students without pets :

total = 41 + 7 = 48

Next, you have to find the ratio of students without pets to total students :

7 : 48

Answer:

SoluTion :-

Total student = Student who have pet + Student who don't have pet

Total Student = 41 + 7

Total Student = 48

Ratio

[tex] \tt \:7 \ratio \: 48[/tex]

I don’t understand this

Answers

Answer:

C = $4.88p

Step-by-step explanation:

You multiply the  number of cheese pounds(p) by the cost of the pounds($4.88)

And you will get your total

Hope this helps!

Your answer should be
C=4.88p

Jake bought 4.08 pounds of apples he then bought 2.19 pounds of oranges how many pounds of fruit did he buy altogether? (SHOW YOUR WORK) place value charts (ONES).(TENTHS) (HUNDREDTHS) (THOUSANDS) also please dont give wrong answers im bad at math ❤️

Answers

Answer:

6.27 lbs

Step-by-step explanation:

Brainliest DONT ANSWER IF YOU NDONT KNOW IT

Answers

Answer:

B

Step-by-step explanation:

THATSS ALL I NOW IT SOO GOOD

You might no
Solve for
9.5 17
AND
13.2 25 1
Choose 1 answer:
-9x+5<17 AND 13x+25<-1

Answers

Answer:

x < -4/3x < -2

Step-by-step explanation:

-9x + 5 < 17

~Subtract 5 to both sides

-9x < 12

~Divide -9 to both sides

x < -4/3

13x + 25 < -1

~Subtract 25 to both sides

13x < -26

~Divide 13 to both sides

x < -2

Best of Luck!

Solve the system:
x + 6y = 17
X - 3y = 8

Answers

Answer: y=1, x=11

Step-by-step explanation: make x in one side in an equation and substitute it in the other and get the value of y then substitute y in one of the equations and get the value of x

x= 8+3y

8+3y+6y=17

9y=9

y=1

X=11

Need help with this problem:
There are two dog runs at the pet store. The first one is 11 3/8 feet long and the second one is 13 2/3 feet long. The owner of the store wants to increase the length of the first one by 4 1/2 feet. She wants to increase the length of the second one by 2 5/12 feet.
1. After the lengths of the dog runs are increased what is the length of the longer dog run?

2. How much longer is the longer dog run than the shorter dog run after the lengths are increased?

Answers

Answer:

1246

Step-by-step explanation:

jk get that work

Please answer this question!!!!! Geometry

Answers

Answer:

i cant see the pic

Step-by-step explanation:

Answer:

I can’t see

Step-by-step explanation:   put it closer

5х2 +х — 4
Factor completely

Answers

Answer:

(5x-4)(x+1)

Step-by-step explanation:

Which symbol will make this multiplication sentence true?
0 × 4 > 0 × 9 or 0 × 4 = 0 × 9
thanks

Answers

Answer:

0 x 4 = 0 x 9

Step-by-step explanation:

Anything times 0 is 0 so they both equal 0

*20 POINTS*

A coffee table is shaped like a square and has an area of 22 square feet. Find the length of the side of the table to the nearest tenth of a foot.

Answers

Answer:

4.69 feet

Step-by-step explanation:

If the table is a square, all the sides are equal and the area is the length of one side squared.  A=l^2

The length must then be the square root of the area. The square root of 22 square feet is 4.6904 feet. Rounded to the nearest tenth, that is 4.69 feet.

Two rectangles with perimeters that are proportional if the area is proportional

Answers

Answer: I'm so sorry, but I'm not sure what you are asking.

I just read your comment, thank you for clarifying, I just was expecting a question, so I didn't really get it. Yeah you are right.

Answer:

Yep

Step-by-step explanation:

Just do that and this then u got it u got to figure out life lol

66.4 mg = blank g

Plz helpppppp !!!!!

Answers

Answer:

0.0664

Step-by-step explanation:

divide the mass value by 1000

PLZ HELP ME IM desperate!!!!
When writing a rebuttal, what is the exact phrasing we use?

Answers

1) Always be polite and professional.

2) Specifically address the points that you disagree with.

3) Provide Evidence.

4) Close with a brief summary of your rebuttal.

Answer:

Although I believe ______, some may think that _______. However (evidence against their claim) shows that (explanation of evidence in 2-3 sentences)

Add or subtract Write in simplest form.
-11/15 - 1/15

Answers

Answer:

- 4/5

Step-by-step explanation:

Step 1:

- 11/15 - 1/15           Equation

Step 2:

- 12/15          Add the negative numbers

Step 3:

- 4/5         Convert

Answer:

- 4/5

Subtracting from a negative number is the same thing as adding them together.

Hope This Helps :)

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