WILL MARK BRAINLIEST!!
I. Write 2-7i in polar coordinates on the complex plane.
II. Find (1+i)^8 using DeMoivre's theorem.
Answers
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
(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
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
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
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
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.
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]PLISSSSSSSS HELPPPPP!!!!!!!!!!!!!!!!!!!!!
I will give brainliest............
Answers
2- 1.5
3- 8
4- 1
5- 5
6- 9
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
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
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:)))
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
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:
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:
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]
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]
6 = $85
18 = ?
18 * 85/6 = 1530/6 = $255
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
add: -38+6+27+(-8)+126
Answers
Answer:
113
Step-by-step explanation:
(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
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
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! :)
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
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
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
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 34Therefore, 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]
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
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
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.
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.
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 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
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.
