WILL MARK BRAINLIEST!!
I. Write 2-7i in polar coordinates on the complex plane.
II. Find (1+i)^8 using DeMoivre's theorem.

WILL MARK BRAINLIEST!!I. Write 2-7i In Polar Coordinates On The Complex Plane.II. Find (1+i)^8 Using

Answers

Answer 1
I. Polar form = (r,θ) = (7.28,254.05°)
z= -2-i7
r= √-2^2+-7^2= √53= 7.28
θ=tan^-1 (-7/-2) =3.5=74.05
Point lies in the third quadrant
Hence θ=180+74.05=254.05°
Polar form = (r,θ) = (7.28,254.05°)

II. Z=16
De Moivre's theorem states if
z= r(cos(θ) + i sin (θ)) , then z^2=r^2(cos(nθ)+
i sin (nθ))
r= √1^2+1^2= √2
θ= arctan (1/1)= π / 4
z= √2 (cos (π / 4)+i sin (π / 4))
z^8 = (√2 (cos (π / 4)+i sin (π / 4)))^8
= (√2 (cos (8π / 4)+i sin (8π / 4)))^8
=16 (cos(2π) + i sin (2π)
=16




Answer 2

(r,θ) = (7.28,254.05°) are 2-7i in polar coordinates on the complex plane.

What are polar coordinates?

The polar coordinates system is a two-dimensional coordinate system in which each point is determined by distance from the point and an angle from the reference direction.

I. Polar form = (r,θ) = (7.28,254.05°)

z = 2 - i7

r= [tex]\sqrt{ 2^2+-7^2}[/tex]

= √53

 = 7.28

θ = tan^-1 (-7/-2)

  =3.5

  = 74.05

Point lies in the third quadrant

Hence θ = 180+74.05

              = 254.05°

Polar form = (r,θ) = (7.28,254.05°)

II. Z=16

De Moivre's theorem states if

z= r(cos(θ) + i sin (θ)) , then

[tex]z^2=r^2(cos(n\theta)+ i sin (n\theta))[/tex]

[tex]r= \sqrt{1^2+1^2}[/tex]

= √2

θ= arc tan (1/1)

  = π / 4

z= √2 (cos (π / 4)+i sin (π / 4))

z^8 = (√2 (cos (π / 4)+i sin (π / 4)))^8

= (√2 (cos (8π / 4)+i sin (8π / 4)))^8

=16 (cos(2π) + i sin (2π)

=16

Learn more about polar form;

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Related Questions

H Solve the following questions.
| Mrs Liya cut a cake into 10 parts and give it out to her 3 children. Liza got the largest parts while Lina got the smallest parts. The difference between the number of parts Liza had and the number of
parts Lina had is equal to the number of parts Lini had. How many
parts did each of them have?

Answers

Answer:

Liza: 5 parts

Lina: 2 parts

Lini: 3 parts

Step-by-step explanation:

Basically, the parts whould equal ten. By following the criteria, Lina must have the least parts, while LIza has the most parts. If the difference between Liza and Lina should be equal to the number of parts Lina had

5-2=3 parts for Lini

Thank you. Tell me if any incorrections.

Is the following statement a good definition? Why?

An obtuse angle is an angle whose measure is greater than 90°.

Answers

Answer:

yes it is all obtuse angles have measures greater than 90°.

Answer:

Yes it is. All obtuse angles have measures greater than 90.

Step-by-step explanation:

Reasoning It has to be Higher then 90 degrees to be called obtuse. This rule applys for all.

At the farmers' market, Lillian bought 5/12 of a pound of string beans and 1/12 of a pound of lima beans. How many more pounds of string beans did Lillian purchase?

Write your answer as a fraction or as a whole or mixed number.

Answers

Answer:

1/3 more pounds of string beans.

Step-by-step explanation:

Amount of string beans: 5/12 of a lbs(pound)

Amount of lima beans: 1/12 of a lbs

Amount of string beans - Amount of lima beans = 5/12-1/12 =4/12 which simplifies down to 1/3.



Sophia worked for 6 hours and got paid $85. How much money did Sophia will earn if she works for 18
hours?

Answers

Answer: $255

Step-by-step explanation:

Use proportions:

[tex]\frac{6hr}{85} =\frac{18hr}{x}[/tex]

Cross-multiply & solve:

[tex]6x=18 * 85\\6x=1530\\x=255[/tex]

she earned $85 for working for 6 hours

6 = $85
18 = ?

18 * 85/6 = 1530/6 = $255

Juan le dice a Laura dentro de 18 años tendré 4 veces la edad que tenia hace 9 años. ¿Qué edad tiene juan?

Answers

Answer:

18

Step-by-step explanation:

18

Someone please help me on this and please tell me the answer directly please !!

Answers

Answer:

0.01

0.05y-0.12y-0.06

Answer:

First one should be: 0.05 + 0.1y = 0.12 + 0.06y

Second one is 100

Step-by-step explanation: Trust me:)))

pls answer with explanation!

The manager of a small baseball stadium uses the equation y = 9000 -2.4x to model the relationship between y, the number of unfilled seats in the
stadium, and x, the number of cars in the parking lot. According to the model, how many cars will be in the parking lot when there are no unfilled seats in the stadium?

Answers

Answer:

3,750 cars.

Step-by-step explanation:

We are given that the equation:

[tex]y=9000-2.4x[/tex]

Models the relationsip between y, the number of unfilled seats in the stadium, and x, the number of cars in the parking lot.

We want to determine the number of cars in the parking lot when there are no unfilled seats in the stadium.

When there are no unfilled seats in the stadium, y = 0. Thus:

[tex]0=9000-2.4x[/tex]

Solve for x. Subtract 9000 from both sides:

[tex]-2.4x=-9000[/tex]

Divide both sides by -2.4:

[tex]x=3750[/tex]

So, there will be 3,750 cars in the parking lot when there are no unfilled seats in the stadium.

Please help me out with this one

Answers

Answer:

[tex]72 cm^{2}[/tex]

Step-by-step explanation:

[tex]===========================================[/tex]

Formulas:

Area of a rectangle/square:

[tex]A=lw[/tex]

Area of a triangle:

[tex]A=bh\frac{1}{2}[/tex]

[tex]===========================================[/tex]

Square:

5*5= 25 cm.

Rectangle#1:

4*5= 20 cm.

Rectangle #2:

3*5= 15 cm.

Triangle (2):

[tex]3*4*\frac{1}{2}=6[/tex]

Multiply by 2 because there are 2 triangles

6*2= 12 cm

Total:

Add them all up.

25+20+15+12= 72

plz help me out with the answer and explaination

Answers

Answer:

7500 m

Step-by-step explanation:

5500 is the initial height. It increased by 1500, so 5500 + 1500 = 7000. Then it went down 2000 meters, so 7000 - 2000 = 5000. It went up 2500 again. 5000 + 2500 = 7500

f(x)=-x^2-9x find f(-2)

Answers

Answer:

14

Step-by-step explanation:

put -2 where x is

f(x)=-x^2-9x

f(-2)= -(-2)^2 -9(-2)

f(-2)= -4 + 18

f(-2)= 14

Point A is located at (-4, -13). Point B is located at (-4, 3). What is the distance between point A
and point B?

Answers

Answer:

the distance is 16

Step-by-step explanation:

Hi there!

We are given point A (-4,-13) and point B (-4,3). We need to find the distance between those two points

the distance formula is given as [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex] where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) are points

we are given 2 points, which is what we need for the formula. However, let's label the values of the points to avoid any confusion

[tex]x_{1}[/tex]=-4

[tex]y_{1}[/tex]=-13

[tex]x_{2}[/tex]=-4

[tex]y_{2}[/tex]=3

now substitute those values into the formula. Remember: the formula uses SUBTRACTION.

[tex]\sqrt{(-4--4)^2+(3--13)^2}[/tex]

simplify

[tex]\sqrt{(-4+4)^2+(3+13)^2}[/tex]

now add the values inside the parenthesis that are under the radical

[tex]\sqrt{(0)^2+(16)^2}[/tex]

raise everything under the radical to the second power

[tex]\sqrt{0+256}[/tex]

add under the radical

[tex]\sqrt{256}[/tex]

now take the square root of 256

[tex]\sqrt{256}[/tex]=16

so the distance between point A and point B is 16

Hope this helps! :)

An ellipse has a co-vertex at (–8, 9) and a foci at (4, 4). If the center of the ellipse is located below the given co-vertex, then what is the equation of the ellipse? Write in standard form. Guide question? 1) What are the coordinates of the center of the ellipse? 2) Is the ellipse horizontal or vertical?

Answers

Answer:

Step-by-step explanation:

“the center of the ellipse is located below the given co-vertex”

Co-vertex and center are vertically aligned, so the ellipse is horizontal.

Equation for horizontal ellipse:

(x-h)²/a² + (y-k)²/b² = 1

with

a² ≥ b²

center (h,k)

vertices (h±a, k)

co-vertices (h, k±b)

foci (h±c,k), c² = a² -b²

One co-vertex is (-8,9), so h = -8.

One focus is (4,4), so k = 4.

Center (h,k) = (-8,4)

c = distance between center and focus = |-8 - 4| = 12

b = |9-k| = 5

a² = c² + b² = 169

(x+8)²/169 + (y-4)²/25 = 1

HELP ASAP!!!

The circle graph shows the percentage of visitors at a
convention who ordered various flavors of juice. There were 700
visitors at the convention.
About how many visitors ordered grape juice or apple juice?
Enter your answer in the box.


Answers

Step-by-step explanation:

40+24+11+8+17= 100

100 - 700

24 - ?

24×700/100

= 168 visitors ordered apple juice

100-700

11-?

11×700/100

=77 people ordered grape juice

How do I find question number 43

Answers

Answer:

[tex]8)79 + .3y |1| 5131x - 2884 \frac{ {8 - { { - 44 - {516}^{ |?| } }^{?} }^{?} }^{2} }{?} 5 - {1 {y {1 {40091 - \times \frac{?}{?} }^{?} }^{2} }^{2} }^{2} 444 = .3 = 547 - 274[/tex]

(6/11) to the power 2 answer pls

Answers

Step-by-step explanation:

in fraction it comes 36/121

and in decimal.it comes 0.3

Answer:

Step-by-step explanation:

6/11^2 = 6/11 * 6/11 = 36 / 121.

You cannot simplify 36/121

Please help me with this problem

Answers

Answer:

Step-by-step explanation:

a*b *c = abc

15c = 15 . c

2a * 10b = 2* 10 * a * b = 20ab

The above mentioned expressions are true

That are false

12ab = 12a * 12b   ----> false because 12ab = 12 * a* b

7a *7b = 14ab is false because   7a * 7b = 7 * 7* a *b = 49ab

rationalization
[tex] \frac{6}{ \sqrt{3} } [/tex]

Answers

Answer:

2√3

Step-by-step explanation:

To rationalize, we multiply the denominator and numerator by the surd at the base

We have it that;

6/√3 * 1

= 6/√3 * √3/√3

= 6 √3/3 = 2√(3

In how many ways can u arrange the letters of the word MATHEMATICS taking three letters at a time?​

Answers

Answer:

256 ways i think maybe

Step-by-step explanation:

Solve for x. Round to the nearest tenth of a degree, if necessary.

Answers

Answer:

[tex]x\approx 49.6^{\circ}[/tex]

Step-by-step explanation:

In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side.

For angle [tex]x[/tex]:

Opposite side is 40Adjacent side is 34

Therefore, we have:

[tex]\tan x^{\circ}=\frac{40}{34}[/tex]

Take the inverse tangent of both sides to solve for [tex]x[/tex]:

[tex]\tan^{-1}(\tan x)=\tan^{-1}(\frac{40}{34}),\\x=\tan^{-1}(\frac{40}{34}),\\x=49.63546343\approx \boxed{49.6^{\circ}}[/tex]

*Recall [tex]\tan^{-1}(\tan x)=x\text{ for } x\in (-90^{\circ}, 90^{\circ})[/tex]

add: -38+6+27+(-8)+126

Answers

Answer:

113

Step-by-step explanation:

Which of the following terms best describes each of the two points marked with dots in the ellipse below?

Answers

Answer:

Focus.

Step-by-step explanation:

.

Answer:

The correct answer is D. Focus.

Step-by-step explanation:

The product of integers a,b,c and d is 546 and if 1<a<b<c<d, what is the value of b+c?​

Answers

Hello,

546=2*3*7*13

a=2, b=3,c=7,d=13

b+c=3+7=10

Need help on this!!! 7 points!!!

Answers

Answer:

P= $226,863.29

Step-by-step explanation:

Compounded Continously means

P= P₀e^(rt)

plug in givens

P=(47000)e^(0.0926*17)

Use Calculator

and get P= $226,863.29

Answer:

$226,863.29

Step-by-step explanation:

P = $47,000

r = 0.0926

t = 17

A = [tex]47,000(2.718)^{(0.0926)(17)}[/tex]

A = $226,863.29

Find the answer to each trigonometric function below. ​

Answers

Answer:

Sin A = [tex]\frac{opposite}{hypotenuse} =\frac{32}{40} =\frac{4(8)}{5(8)} =\frac{4}{5}[/tex]Cos C = [tex]\frac{adjacent}{hypotenuse} =\frac{16}{34}=\frac{2(8)}{2(17)} =\frac{8}{17}[/tex]Tan A = [tex]\frac{opposite}{adjacent} =\frac{21}{20}[/tex]

Tony is 3 years older than Marie. This can be modeled with the following equation

Answers

Answer:

M = T - 3

Step-by-step explanation:

Given

T = M + 3 ( subtract 3 from both sides )

T - 3 = M , that is

M = T - 3

Answer:

[tex] \small \sf \: M = { \fbox { \green{T} } } - 3[/tex]

Step-by-step explanation:

T = M + 3

Swap the sides of of equations .

M + 3 = T

subtract 3 from both side

M + 3 - 3 = T - 3

M = T - 3

PLISSSSSSSS HELPPPPP!!!!!!!!!!!!!!!!!!!!!
I will give brainliest............

Answers

I know the square root of sixteen is 4
1- 4
2- 1.5
3- 8
4- 1
5- 5
6- 9

Marcos buys a pumpkin that weighs 1.37 pounds. Gabriel buys a pumpkin that weighs 0.24 pounds more than Marcos' pumpkin. How much does Gabriel's pumpkin weigh, in pounds?

Answers

Answer:

1.61 pounds

Step-by-step explanation:

Weight of Marcos pumpkin = 1.37 pounds

Weight of Gabriel's pumpkin = Weight of Marcos pumpkin + 0.24 pounds

= 1.37 pounds + 0.24 pounds

= 1.61 pounds

Weight of Gabriel's pumpkin = 1.61 pounds

vedanta Excel In Opt. Mathematics - Book 9
Find the locus of a point which moves so that

(a) Its distance from (1, 2) and (2, -3) are equal.​

Answers

(1 , 2) (2, -3) (x1,y1) (x2, y2)

Distance formual √(x2-x1)+(y2-y1) {substitute numbers in formula}

= √(2-1)^+(-3-2)^ =√(1)^+(-5)^ [here square root and square get cancelled] = (1)+(-5) = 1-5 = -4
A point that is equidistant from two points will travel along the perpendicular bisector of the line that joins them.
The gradient of the line between (1,2) and (2,-3) is (-3 - 2)/(2 - 1) = -5
The perpendicular gradient = -1/-5 or 0.2
The midpoint between (1,2) and (2,-3) is ((1+2)/2,(2+-3)/2) = (1.5, -0.5)
Substituting into y=mx + c
-0.5 = 0.2 x 1.5 + c
-0.5 = 0.3 + c
c = -0.5 - 0.3 = -0.8
So the locus is the line y = 0.2x - 0.8

8 Find the value of x a (22²)x is exponent of (22²) = 64​

Answers

Given:

Consider the given equation is:

[tex](2\cdot 2^2)^x=64[/tex]

To find:

The value of x.

Solution:

We have,

[tex](2\cdot 2^2)^x=64[/tex]

It can be written as:

[tex](2\cdot 4)^x=8\times 8[/tex]

[tex]8^x=8^2[/tex]

On comparing the exponents of both sides, we get

[tex]x=2[/tex]

Therefore, the value of x is 2.

The function f(x) is a quadratic function and the zeros of f(x) are 1 and 5. The y-intercept of f(x) is 20. Write the equation of the quadratic polynomial in standard form.

Answers

Answer:

4x² - 24x + 20 = 0

Step-by-step explanation:

a(1)² + b(1) + 20 = 0

a(5)² + b(5) + 20 = 0

a + b = - 20 ⇒ b = - a - 20 ...... (1)

25a + 5b = - 20 .......... (2)

(1) -----> (2)

25a + 5( - a - 20) = - 20

20a - 100 = - 20 ⇒ a = 4

4 + b = - 20 ⇒ b = - 24

4x² - 24x + 20 = 0

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