Describe the set of all complex numbers that are at a distance of 2 units from the origin.

Answers

Answer 1

Answer:

The description of the set is [tex]A = \{s\in \mathbb{C}|\|s\| = 2\}[/tex].

Step-by-step explanation:

From Complex Analysis, we remember that complex numbers are numbers whose form is:

[tex]s = a+i\, b[/tex], [tex]a,b \in \mathbb{R}[/tex] (1)

Where [tex]i = \sqrt{-1}[/tex].

In addition, the distance from the origin is defined by the following Pythagorean identity:

[tex]\|s\| = \sqrt{a^{2}+b^{2}}[/tex] (2)

The following condition must be satisfied:

[tex]\|s\| = 2[/tex]

Then, the set of all complex numbers that are at a distance of 2 units from the origin is described below:

[tex]A = \{s\in \mathbb{C}|\|s\| = 2\}[/tex] (3)

Answer 2

The set of all complex numbers that are at a distance of 2 units from the origin is [tex]\{z\in \mathbb{C} :\text{ }|z|=2\}[/tex]

A complex number, written in rectangular form is

[tex]z=a+ib\\a,b\in \mathbb{R}[/tex]

The distance of a complex number from the origin (the modulus of the complex number, denoted by [tex]|z|[/tex]) is given by the formula

[tex]|z|=\sqrt{a^2+b^2}[/tex]

Since we want all the complex numbers to be at the distance of 2 units from the origin, they must satisfy

[tex]|z|=2[/tex]

thus, the set we are looking for is

[tex]D=\{z\in \mathbb{C} :\text{ }|z|=2\}[/tex]

where [tex]\mathbb{C}[/tex] is the set of all complex numbers

Learn more about complex numbers here: https://brainly.com/question/12274048


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2x-Y (5y X -6) 3^6y what is that as an expression

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Answer:

The answer is:

2x + 30y^2 × 729^y

Which of the following expressions is equivalent to 3m(m - 2) - (m^2 + 1)
A. 2m^2 - 1
B. 4m^2 - 1
C. 4m^2 - 6m + 1
D. 2m^2 - 6m - 1

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I think the answer must be b

that is the question

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You have them all marked

Use the​ slope-intercept form to graph the equation y=3/7x+3

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here you go

Step-by-step explanation:

what is the Symmetric property

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Answer:

The Symmetric Property states that for all real numbers x and y , if x=y , then y=x . Transitive Property. The Transitive Property states that for all real numbers x ,y, and z, if x=y and y=z , then x=z .

Step-by-step explanation: you couldnt have looked it up on ggle?...haha -_-'

A pancake mix requires 5 cups of flour for every 10 pancakes. How much flour is used per pancake?

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So you have 5 cups of flour for 10 pancakes so what you want to do is just divide 10 by 5 and you get your answer of 2 :)

89 x 89, whats the answer?

Answers

Answer:

7921 is the correct answer

Answer:

7,291

Step-by-step explanation:

Just multiply. 89 x 89

               

                     

Find the next term of the given sequence. 1.31, 2.54, 3.77, ...
4.90
5.00
5.10

Answers

The answer would be: 5.00
It’s adding by 1.23

Answer:

5.00

Step-by-step explanation:

HELP! i can not figure this out! y=4x+1

Answers

Answer:

1

Step-by-step explanation:


Michael started a savings account with $300. After 4 weeks, he had $350 dollars, and after 9 weeks, he had $400. What is the rate of
change of money in his savings account per week?
Person to answer get prize
Pls help

Answers

Answer:

$12.5

Step-by-step explanation:

all you do is divide the 4 weeks to the $50 he earns and get $12.5 every week.

Hello, please, I need the answers!! Each year a school booster club holds a dance to raise funds. In the past, the profit of the club makes after paying for the bank and other costs has been modeled by the function p(t) = -16t^2 - 800t - 4000 where t represents the ticket price in dollars. a. What ticket price gives the maximum profit? b. What is the maximum profit? c. What ticket prices would generate a profit of $5000?

Answers

Answer:

Step-by-step explanation:

Given the profit a club makes after paying for the bank and other costs modeled by the function

p(t) = -16t^2 - 800t - 4000

t is the ticket price

The maximum profit occurs when dp/dx = 0.

dp/dx = -32t-800

since dp/dx

0 = -32t-800

32t = -800

t = -800/32

t = - 25

Hence ticket price gives the maximum profit is $-25

b) to get the maximum profit, substitute t = -25 into the modelled function

p(t) = -16t^2 - 800t - 4000

p(-25) = -16(-25)² - 800(-25)- 4000

p(-25) = -10000+20000-4000

p(-25) = 6000

Hence maximum profit is $6000

c) To get the ticket prices would generate a profit of $5000, we will substitute p(t) = 5000 and find t

p(t) = -16t^2 - 800t - 4000

5000 = -16t^2 - 800t - 4000

-16t^2 - 800t - 4000 -5000 = 0

16t^2 + 800t + 9000 = 0

Answer:

Step-by-step explanation:

Given the profit a club makes after paying for the bank and other costs modeled by the function

p(t) = -16t^2 - 800t - 4000

t is the ticket price

The maximum profit occurs when dp/dx = 0.

dp/dx = -32t-800

since dp/dx

0 = -32t-800

32t = -800

t = -800/32

t = - 25

Hence ticket price gives the maximum profit is $-25

b) to get the maximum profit, substitute t = -25 into the modelled function

p(t) = -16t^2 - 800t - 4000

p(-25) = -16(-25)² - 800(-25)- 4000

p(-25) = -10000+20000-4000

p(-25) = 6000

Hence maximum profit is $6000

c) To get the ticket prices would generate a profit of $5000, we will substitute p(t) = 5000 and find t

p(t) = -16t^2 - 800t - 4000

5000 = -16t^2 - 800t - 4000

-16t^2 - 800t - 4000 -5000 = 0

t^2 + 50t + 562.5= 0

Factorize

-50±√2500-4(562.5)/2

t = -50±√2500-2250)/2

t = -50±15.81/2

t = -65.81/2 and -34.19/2

t = -32.91 and -17.09

The next model of a sports car will cost 14.1% less than the current model. The current model costs $55,000 . How much will the price decrease in dollars? What will be the price of the next model?

Answers

Answer:

$3900.71 is the amount of money subtracted from the next model

51099.29 is the cost of the second model

Step-by-step explanation:

You buy a watch for $60. a. There is a 6% sales tax. What is your total cost for the watch? b. Your friend buys the same watch a month later. It is now sold at a discount of 15%. What is the new sale price? c. What is your friend's total cost for the watch including tax? Original Price Percent of Discount Sale Price is?

Elizabeth Martz

Answers

Answer:

A= 63.6$

B= 51$

C= 54.6

D= ??? (sorry)

Step-by-step explanation:

hope this helps!

The answers to each part is given below.

What is percentage?

In mathematics →

a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".

Given is that you buy a watch for $60.

{a} -

Total cost of watch -

{C} = ${60 + (6% of 60)}

{C} = ${60 + (6/100 x 60)}

{C} = $(60 + 3.6}

{C} = $63.6

{b} -

New sale price -

{D} = 60 - (15% of 60)

{D} = 60 - (15/100 x 60)

{D} = 60 - 9

{D} = $51

{c} -

Total cost of watch including tax -

{CT} = 51 + (6% of 51)

{CT} = 51 + 3.06

{CT} = 54.06

Therefore, the answers to each part is given above.

To solve more questions on percentage, visit the link below -

brainly.com/question/24159063

#SPJ2

Helpp!
Shamir is trying to decide between two cities to travel to for a weekend trip. The prices for a hotel room for two nights and the hotel tax rate are listed in the table
| city | cost ($) | Tax rate |
| A | 250 | 12.5% |
| B | 215 | 14.75% |
What is the difference in cost between the two cities for a weekend trip? Round to nearest cent

Answers

Answer:

$34.54

Step-by-step explanation:

city A

$250 x 1.125 $281.25

city B

$215 x 1.1475 $246.713

difference between the two cities = $281.25 - $246.713

                                                        = $34.54

The difference in cost between the two cities for a weekend trip will be $34.54.

What is the percentage?

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

Shamir is trying to decide between two cities to travel to for a weekend trip. The prices for a hotel room for two nights and the hotel tax rate are listed in the table.

City                Cost ($)             Tax rate

A                     $250                12.50%  

B                     $215                  14.75%

Then the difference in cost between the two cities for a weekend trip will be given as,

⇒ $250 × 1.1250 - $215 × 1.1475

⇒ $281.25 - $246.71

⇒ $34.54

The difference in cost between the two cities for a weekend trip will be $34.54.

More about the percentage link is given below.

https://brainly.com/question/8011401

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Which equation is represented by the graph below?

Answers

Answer: 2/3 x +6

Step-by-step explanation:

slope is 2/3 and y intercept is 6

g(n) = 4n +4
h(n) = n +5
Find (g- h) (9)

Answers

Answer:

3n-1

Step-by-step explanation:

(4n+4) - (n+5)

i sperate it to be

4n-n and 4-5

so

3n-1 should be it

help!!! please & explain if can:(

Answers

Answer:

x = 15

Step-by-step explanation:

AEB is a right angle, a right angle is 90 degrees

this means 5x+15 needs to equal 90

plug in 15 for x

5 x 15 + 15 = 90

Plz help with the math question

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Answer:

the answer is 20

Can someone help me with this question

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Answer B
I could be wrong
Explanation

Answer:

c is the right one

Step-by-step explanation:

As you can see I NEED HELP RIGHT NOW!

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Answer:

Ten over two would be at the very right side of this number line. It would be located at the number 5. Negative nine over two would be located two segment or lines after negative five.

Step-by-step explanation:

Ten over two would come out to a positive and whole number of five. Negative nine over ten comes out so negative four wholes and one half. So this gets located two segments after negative five because it is not fully negative five but it is negative four and one half. I got these whole numbers by simplifying the numbers that we started off with. Hope you have an amazing day and do well on your assignments.

-Vizion

This is the correct answer!

solve 3(x-4) = 12x. circle your final solution

Answers

Answer:

9x-12

Step-by-step explanation:

3*x = 3x

3*-4= -12

3x - 12 = 12x

12x-3x = 9x

9x-12

Answer:  x = -4/3

Step-by-step explanation:

3(x−4)=12x

Step 1: Simplify both sides of the equation.

3(x−4)=12x

(3)(x)+(3)(−4)=12x  (Distribute)

3x+−12=12x

3x−12=12x

Step 2: Subtract 12x from both sides.

3x−12−12x=12x−12x

−9x−12=0

Step 3: Add 12 to both sides.

−9x−12+12=0+12

−9x=12

Step 4: Divide both sides by -9.

-9x/-9 = 12/-9

x = -4/3

1.4y+5-4.2-5y^2+z
It has something to do with combing like terms
Identify the number of terms, variable terms and constant terms in the following expression.

Answers

Answer:

Step-by-step explanation:

[tex]4y+5-4.2-5y^{2}+z[/tex]

constant terms: 5 and -4.2 equals 0.8

No matching variable terms.

[tex]-5y^{2} + 4y+z+0.8[/tex]

4 total terms

Luis bought stock at $63.30. The next day, the price increased $12.80. This new price changed by −6 3/4% the following day. What was the final stock price, rounded to the nearest cent? Is your answer reasonable? Complete the explanation.

Answers

hold on gimmie a sec and I’ll get back

Which of the following describe 4/8

Answers

Answer:

4/8 is one half.

Step-by-step explanation:

4/8 -- 4 goes into both the numerator and denominator -- 4 goes into 4 one time and 4 goes into 8 two times.

Therefore, you have 1/2.

Answer:

4/8=.5 or 1/2

Step-by-step explanation:

4/8 can be reduced to 1/2

9/2 ÷ 3/4
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The answer will be 6

Please answer this question shown in the picture! Thank you soooo much if you do! ;w;

Answers

Answer:

3.07 . 10^8.

Step-by-step explanation:

2.3 . 10^8 + 4.7 . 10^7

= 230,000,000 + 77,000,000

= 307,000,000

= 3.07 . 10^8.

please help me asap

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It’s A because you add the numerator and denominator

Find 4+(−1 2/3). Write your answer as a fraction in simplest form.

Answers

Answer:

[tex]\frac{7}{3}[/tex]  

I hope this helps!

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2 1/3

Step-by-step explanation:

Graph the following inequality:

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Step-by-step explanation:

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Not too sure, but I think X = 39
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