Consider the numbers z = 3√2(cos(135°) + i sin(135o) and w = cos(180o) + i sin(180°).
Which expression is closest to the polar form of z + w?

Consider The Numbers Z = 32(cos(135) + I Sin(135o) And W = Cos(180o) + I Sin(180).Which Expression Is

Answers

Answer 1

Answer: A

5(cos(143o) + i sin(143o))

Step-by-step explanation:

Answer 2

The expression that is closest to the polar form of z + w is

[tex]5(cos(143^{\circ})+i~sin(143^{\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 polar form of the complex number?

"The polar form of the complex number z = x + iy is [tex]z=r(cos(\theta)+i~sin(\theta))[/tex] where [tex]r=\sqrt{x^{2} +y^{2} } , ~\theta=tan^{-1}(\frac{y}{x} )[/tex] "

For given question,

We have been given two complex numbers.

[tex]z = 3\sqrt{2} (cos(135^{\circ}) + i~sin(135^{\circ})[/tex] and [tex]w = cos(180^{\circ}) + i~sin(180^{\circ})[/tex]

We know that,

[tex]cos(135^{\circ})\\=cos(90^{\circ}+45^{\circ})\\=-sin(45^{\circ})\\=-\frac{1}{\sqrt{2} }[/tex]

And

 [tex]sin(135^{\circ})\\=sin(90^{\circ}+45^{\circ})\\=cos(45^{\circ})\\=\frac{1}{\sqrt{2} }[/tex]

So, the first complex number would be,

[tex]z = 3\sqrt{2} (cos(135^{\circ}) + i~sin(135^{\circ})\\\\z = 3\sqrt{2} (-\frac{1}{\sqrt{2} } + i~\frac{1}{\sqrt{2} } )\\\\z=-3+3i[/tex]

We know that [tex]cos(180^{\circ})=-1,~~sin(180^{\circ})=0[/tex]

So the second complex number would be,

[tex]w = cos(180^{\circ}) + i~sin(180^{\circ})\\\\w = -1 + 0i[/tex]

So, the sum of complex numbers z and w would be,

[tex]z+w\\=(-3+3i)+(-1+0i)\\=-4+3i[/tex]

We write the complex number -4 + 3i in the polar form.

Comparing above number with x + iy, we have x = -4 and y = 3

[tex]\Rightarrow r=\sqrt{(-4)^2+3^2}\\ \Rightarrow r=5[/tex]

Also, the value of [tex]\theta[/tex] would be,

[tex]\theta=tan^{-1}(\frac{3}{-4} )\\\\\theta= -36.86^{\circ}\\\\\theta=180^{\circ}-36.86^{\circ}\\\\\theta=143.14^{\circ}[/tex]

So the complex number -4 + 3i in the polar form would be, [tex]5(cos(143.14^{\circ})+i~sin(143.14^{\circ}))[/tex]

Therefore, the expression that is closest to the polar form of z + w is

[tex]5(cos(143^{\circ})+i~sin(143^{\circ}))[/tex]

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Related Questions

22a) PLEASE HELP BEST ANSWER BRAINLIEST

Endpoints of segment MN have coordinates (0, −3), (−2, −4). Endpoints of segment AB have coordinates (2, 5), (4, k).
a
What value of k makes these segments perpendicular?

Answers

Answer:

the answer is k=1

Step-by-step explanation:

log_6⁡(x+1)+log_6⁡x=1

Answers

This is pretty simple once you figure out the trick.

All you have to do is make the args common.

Meaning [tex]log_{6}(x + 1) + log_{6}(x) = 1[/tex] is nothing but [tex]log_{6}(x(x + 1)) = 1[/tex]

Which is nothing but: [tex]log_{6}(x^2 + x) = 1[/tex].

Now using the scorpion tail method, this equation can be reframed to being: [tex]6 = x^2 + x[/tex]. You bring 6 to the other side and it'll become: [tex]x^2 + x - 6 = 0[/tex]

Factorise it and you get: [tex](x - 2) * (x + 3)[/tex]

Henceforth, the solution would be [tex]2[/tex] and [tex]-3[/tex]. :D

Answer:

D. x = 9

Step-by-step explanation:

edge 2022

A meteorologist records the temperature as - 7.5°C at 7 a.m. and as-4.3°C at 10p.m. Which statement is true?

Answers

Answer:

Step-by-step explanation:

its maybe A

elena receives $200 for a birthday present, which she deposited in a bank account. Every month she withdraws $25. how much will she have left in her bank?

Answers

Answer:

8 months

Step-by-step explanation:

for every 100 four 25s and these two 100s so 8

hope this helps

graph the line with the equation y=-6/5x+1

Answers

See attachment for answer:

pls help pls ill mark brainliest

Answers

Answer:

Area/Circumference is the length of a circle!

Step-by-step explanation:

Answer: the answer is area/ circumference

Step-by-step explanation:

Given f(x) = 7 - 4x. If the domain of the function is {-4, 0, 1.75, 3}, what is the range of the function?

Answers

Answer:

[-5,23]

Step-by-step explanation:

f(-4)=23

f(3)= -5

put the maximum and minimum values for x which at domain

To complete her holiday wrapping, bella needs identical strips of ribblon measuring 3.5 feet each. She has 85 feet of ribbon in total. About how many pieces of ribbon can she cut from this long strip

Answers

Answer:

85/3.5 = 17/0.7 = 24.29  pieces of ribbon .

Step-by-step explanation:

Is 1¾ a rational numbers​

Answers

Answer:

Yes 1¾ is a rational number

Step-by-step explanation:

1¾ is written as a fraction of two integer and is therefore rational.

A dime (0.10) is what percent of a dollar (1.00)?

Answers

10%.
1.00 / 0.10 = 10

Answer:

10%

Step-by-step explanation:

Question 1 of 10
What is the slope of the line shown below?
10
(3,9)
O A.
5
B. 4
(1,1)
-5
10
15
O C. -
1
4
O D.-4
SUBMIT

Answers

I’m pretty sure it’s B because of rise over run.

The slope of the given line is 4.

What is slope?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Given that, a line passing through points (3, 9) and (1, 1) we need to find the slope of the line,

Slope = y₂ - y₁ / x₂ - x₁

So,

Slope = 9-1 / 3-1 = 8/2 = 4

Hence, the slope of the given line is 4.

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how to get beter at maths

Answers

Try to understand the problem and take everything step by step

Answer:       to get better in math:-

i) listen to the math class properly

ii) practice the math works thoroughly

iii) do homeworks on time

iv) if there is any doubt still feel free to ask to the teacher

v) do revision of the taken chapters once in month

vi) If u can attend tuition classes then attend them

doing these steps I'm sure u can be better in math.

Hope it helped u, pls mark this as brainliest and put thanks for the ans

How do you do these questions?

Answers

Part (a)

The equilibrium price occurs at the intersection of the supply and demand curves. See the diagram below to see how this looks. Ignore the red line and green lines for now. Those will apply for part (b).

If the price was below equilibrium, then we would have a shortage and it would lead to a pressure to push prices upward. If the price was below equilibrium, then there would be a surplus or oversupply, leading to a downward pressure in prices. So inevitably the price lands on the equilibrium if given enough time and there are no external forces acting on the market.

==============================================================

Part (b)

Let's say we have two people labeled person A and person B. If person A gets a higher education, while person B does not, then person A is likely to earn more money. Person B will see this and want to may want to earn more money as well, so that makes their demand for higher education go up.  While of course this rule doesn't work for everyone, in general we'll have enough people to effectively push the demand curve to the right while the supply curve remains where it is. Check out the diagram below to see what I mean.

==============================================================

Part (c)

Refer to the diagram in part (b). We have a new demand curve which intersects the supply curve to produce a new equilibrium point with price P1 and quantity Q1. So effectively the tuition has gone up due to higher demand.

==============================================================

Part (d)

If a government provides a subsidy, then this would lower the cost of education to provide people with more opportunities to improve their earning potential. The subsidy would provide a portion of the tuition which gives the illusion of the tuition price being lowered. In a way it's like getting a grant from the government to then pay that money toward your tuition.

Which algebraic expression is equivalent to the expression below? 6(3x - 4/3) + 44

A. 18x - 36

B. 18x - 52

C.18x + 52

D.18x + 36

Answers

Answer:

D

Step-by-step explanation:

first distribute 6 to get

(18x - 8) +44

combine like terms

18x + 36

Answer: D.) 18x+36

-4/3×6=-8

-8+44=36

6×3x=18x

I hope this is good enough:

Use the digits 5, 3 and 2 two only once in each number how many different three digit numbers can you make

Answers

53, 52, 35, 32, 25, 23

3/4x+2-1/3x=12
What is the answer?

Answers

Answer:

x=24 or 25

Step-by-step explanation:

90% is x=24

89.999999 repeat% is x =25

Mary keeps track of how much time she goes running each week for 10 weeks. the frequency table with the data she collected. How many hours did mary spend​ running?

Answers

Answer:

One bad b, and she do what I say so

Two big .40s and a big a Draco (two, boom, boom)

Three more millions when you ask how my day go

Poured up a 4, now that's blueberry Faygo

One false move, and we straight to shooting s

Two small bands just to take you out real quick (bands)

Three more h, pull up, I'm f s

That's how it go, big bands, I'm thumbin' s (that's how it goes)

One bad b, and she do what I say so (yeah, gang)

Two big .40s and a big a Draco (two)

Three more millions when you ask how my day go

Poured up a 4, now that's blueberry Faygo

One false move, and we straight to shooting s

Two small bands just to take you out real quick (bands)

Three more h, pull up, I'm f s

That's how it go, big bands, I'm thumbin' s

I'm with my n*yeah, we some rockstars

And I'm with my n yeah, KK Wokhardt (KK Wokhardt)

This not my d, lil' b, my Glock hard (lil' b)

Straight to the cash, I'm a trapstar (cash)

Straight to the bag, I'm that n, huh (bag, oh)

Got me some gas, rollin' up some

Fft, fft, cash, yeah, I got me some

I ain't f her yesterday (yeah)

I'ma f some

One bad b , and she do what I say so

Two big .40s and a big a Draco (two, boom, boom)

Three more millions when you ask how my day go

Poured up a 4, now that's blueberry Faygo

One false move, and we straight to shooting s

Two small bands just to take you out real quick (bands)

Three more h, pull up, I'm f s

That's how it go, big bands, I'm thumbin' s (that's how it goes)

3-0 clip in my Nina (oh, oh)

On my toes, Gucci, Valentino (yeah, b)

She on go, your b f the team, uh (lil' b )

'Cause you know your b want a winner (winner)

I just went back to my city (to my city)

And you know they all f with me (big hands)

But it ain't safe, h with me (h)

I'ma chase bands 'til they end me

One bad b, and she do what I say so

Two big .40s and a big a Draco (two, boom, boom)

Three more millions when you ask how my day go

Poured up a 4, now that's blueberry Faygo

One false move, and we straight to shooting s

Two small bands just to take you out real quick (bands)

Three more h, pull up, I'm f s

That's how it go, big bands, I'm thumbin' s (that's how it goes)

One bad b, and she do what I say so (yeah, gang)

Two big .40s and a big a Draco (two)

Three more millions when you ask how my day go

Poured up a 4, now that's blueberry Faygo

One false move, and we straight to shooting s

Two small bands just to take you out real quick (bands)

Three more h, pull up, I'm f s

That's how it go, big bands, I'm thumbin' s

Step-by-step explanation:

Read the excerpt from "Myths About the Founding Fathers This is the truth Revere did ride from Boston to Lexington to warn Hancock and Adams, but he didn't go alone William Dawes took a different route to Lexington, joining Revere and Dr. Samuel Prescott. All three had been spreading the word that the regulars are coming along the way. There may have been as many as forty others who helped.

How do these sentences contribute to the development of ideas in the passage?

It explains how myths about Paul Revere came to

It highlights the importance of lessons to be learned from myths

It provides evidence that Revere's actions were exaggerated in myths

It shows that this are often based on real events​

Answers

Answer: it shows that myths are often based on real events. Hope it helps

Step-by-step explanation:

i took the test on the k-12 site and the was the answer cuz i got it correct.

three-fourths of a number is at least -18​

Answers

Answer:

3/4*X < -18

( put a line underneath the less than sign ) ( Astric's means multiplication )

Step-by-step explanation:

Hope this helped, Have a Wonderful Day!!

Answer:

x ≥ - 24

Step-by-step explanation:

Let's solve this with an equal sign and then decide how to handle the at least part.

3/4 x = -18              Multiply by 4

3/4 * 4 x = -18*4     Cancel the left, multiply the right.

3x = -72                  Divide by 3

x ≥ -24

You need  the greater than to indicate that 3/4 of a number can give something larger than - 18.

You need the equal sign to fulfill at least.

At least, in this question means "get larger."

so x > - 24

How can you solve linear equations and inequalities in one variable, including equations with coefficients represented by letters?

Answers

Answer:

X=3

Step-by-step explanation:

For a linear equation like 2x + 3 = 9 you would start with subtracting 3 from both sides. Then you would divide both sides by 2 to get x by itself. You get x=3

For linear inequalities it’s the same but with a less than or equal sign. You just solve the same way. However if you divide a negative the sign flips like in my second example. I’m not sure if this is exactly what you are looking for since I don’t know what your problems look like but I hope it helps.

sneakychickens please help​

Answers

i believe the answer is 48.

Answer:

16

Step-by-step explanation:

First I plugged in the values like [tex](-2)^{2} |6-(3(-2))|[/tex]

Then I Solved [tex](-2)^{2}[/tex] and got 4

Than I multiplied 3 by -2 and got -6

Now the equation looks like 4|6-(-6)| which will now be 4|6+6|

then add 6 and 6 together and you get 12 now you add 4 and 12 together and you get your answer 16

Hope this helps

Adele mows lawns in her neighborhood each weekend to save money for college.She uses her parents lawn mower,but is responsable for buying gas and other supplies she’ll need.The table below shows her profit after the first two lawns she moved last weekend.Adele charges the same amount of every lawn she mows.Select the function that models the relationship between her profit and the number of lawns she mows.

Answers

Answer:

P = 25m - 15

Step-by-step explanation:

Kindly find attached the table of values for your reference.

Step one:

given data

let us set up the coordinate using the value of p and m

p=35

p1=10

m=2

m1=1Tthe cordinate is (p1,p),(m1,m)= (y1,y),(x1,x)

(1,10), (2, 35)

the slop is given as, slope m = (p- p1)/(m - m1)

m=(35-10)/(2-1)

m = 25

from the equation of line y=mx+c

y = 25x + c

10 = 25(1) + bc

c= -15

y = 25x - 15

in term of m and p we have  P = 25m - 15

1) g(x) = 4x + 3
h(x) = 3x + 3
Find g(x) + (x)

Answers

Answer:

Step-by-step explanation:

g(x) = 4x + 3

h(x) = 3x + 3

g(x) + h(x) = 7x + 6

what is 5/ 16 expressed as a percentage ​

Answers

Answer:

31.25%

Step-by-step explanation:

To express a number as a percent we will first divide the top number by the bottom number.

5/16 = 0.3125

A percent is expressed by moving the decimal two places to the left.

31.25%

Estimate the following sum by first rounding each decimal to the nearest hundred. Is the answer 800?

Answers

Which sum are we supposed to round?


Anyone???

Mathematics

Answers

The slope is rise over run
The rise is 1
The run is 2
So the slope would be 1/2

Is line l parallel to line m? Explain.
Yes, alternate interior angles are congruent.
No; alternate interior angles are not congruent.
No; corresponding angles are not congruent.
Yes; corresponding angles are congruent.

Answers

Answer:

yes, corresponding angles are congruent

Step-by-step explanation:

The given equation shows the relationship between the price, in dollars, y, of x gallons of gasoline.
y = 2.251
Which graph represents the proportional relationship?
Cost of Gasoline
3.5
Cost of Gasoline
3.5
3
3
2.5
2.5
Price ($)
2
Price ($)
2
1.5
1.5
1
1
0.5
0.5
0
0
0.5 1 1.5 2 2.5 3 3.5
Gallons of Gasoline
w.
0.5 1 1.5 2 2.5 3 3.5
Gallons of Gasoline
X.
Cost of Gasoline
Cost of Gasoline
Y
3.5
3.5
3
3
2.5
2.5
Price ($)
2
Price ($)
2
1.5
1.5
1
1
0.5
0.5
0
0
0.5 1 1.5 2 2.5
1.5 2 2.5 3 3.5
Gallons of Gasoline
Y.
0.5 1 1.5 2
1.5 2 2.5 3 3.5
Gallons of Gasoline
z.
1 of 10 Answered
Session Score: 0% (0/1)

Answers

It would be Z and X bc they match up with each other they are just on different parts of the graph

help plsss hurryyyyyy

Answers

the answer is y=-x+6

Tyler is packing his bags for vacation. He plans to pack two outfits for each day of vacation.
Let d = the number of days of his vacation.
Write an expression for the total number of outfits WILL BRIANLIST

Answers

Answer:  2d

=========================================

Work Shown:

d = number of days of his vacation

1 day = 1*2 = 2 outfits

2 days = 2*2 = 4 outfits

3 days = 3*2 = 6 outfits

4 days = 4*2 = 8 outfits

5 days = 5*2 = 10 outfits

and so on.

In general we can say,

d days = d*2 = 2d outfits

d is simply a placeholder or a box where we'll place a number inside. For example, if he's on vacation for d = 7 days, then he'll bring 2*d = 2*7 = 14 outfits.

The expression 2*d is the same as 2d. We can leave out the multiplication sign since having a number next to a variable like this implies multiplication.

The expression for the total number of outfits is 2d

The total number of outfits Tyler plans to pack for his vacation can be expressed as 2 multiplied by the number of days of his vacation, which we'll denote as 'd'. Since Tyler plans to pack two outfits for each day, multiplying 'd' by 2 will give us the total number of outfits.

In this expression, 'd' represents the number of days of Tyler's vacation, and multiplying it by 2 accounts for the two outfits planned for each day. This expression allows us to calculate the total number of outfits based on the length of Tyler's vacation.

For example, if Tyler's vacation is 7 days long, the expression 2d would yield:

2 * 7 = 14

Therefore, Tyler would plan to pack 14 outfits for his 7-day vacation. The expression 2d allows flexibility to calculate the total number of outfits based on the specific number of vacation days.

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