![Which Number Represents A Square Root Of 3 [cos(pi/2) + I Sin (pi/2)]?](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/MqWXL71zCVe43DIpTiqE5ufnn3R25BHp.png)
Answers
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Explanation:
We use De Moivre's Theorem. It says that if you started with
[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]
then raising both sides to the nth power leads to
[tex]z^n = r^n*\left[\cos\left(n*\theta\right)+i*\sin\left(n*\theta\right)\right][/tex]
The term out front r is raised to the nth power. We also have copies of n inside the trig functions.
The square root operation undoes the squaring operation, so we'll be dealing with n = 2.
If you were to go through each answer choice, then you'll find that squaring choice B will lead to the original expression given.
[tex]z = \sqrt{3}*\left[\cos\left(\frac{\pi}{4}\right)+i*\sin\left(\frac{\pi}{4}\right)\right]\\\\\\z^2 = (\sqrt{3})^2*\left[\cos\left(2*\frac{\pi}{4}\right)+i*\sin\left(2*\frac{\pi}{4}\right)\right]\\\\\\z^2 = 3*\left[\cos\left(\frac{\pi}{2}\right)+i*\sin\left(\frac{\pi}{2}\right)\right]\\\\\\[/tex]
Note that working this process in reverse means we apply the square root and we'll go from the expression in choice B to the original expression again.
The complex number Z = √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number in the trigonometric form:
Z = √(3[cosπ/2 + i sinπ/2])
It is required to find the square root of the complex number.
To find the square root of the complex number we can use the De Moivre's theorem:
If
Z = r[cosθ + i sinθ]
Zⁿ = rⁿ[cosnθ + i sinnθ]
Using the above theorem:
Z = √3[cos[(1/2)π/2] + i sin[(1/2)π/2]]
Z = √3[cosπ/4 + i sinπ/4]
Thus, the complex number Z = √3[cosπ/4 + i sinπ/4] represents the complex number √(3[cosπ/2 + i sinπ/2]) after using the De Moivre's theorem option (B) is correct.
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Related Questions
Help me with this hw plzzz
Answers
Use point-slope form to write the equation of a line that passes through the point
(-3, -16) with slope – 2/1
Answers
Answer:
y= -2x-22.
Step-by-step explanation:
1) the slope-interception common form is y=s*x+i, where 's' and 'i' are the slope and interception, unknown numbers;
2) if x₁= -3; y₁= -16, and s=-2, then the equation of the required line can be written in the point-interception form y-y₁=s(x-x₁); ⇔ y+16= -2(x+3);
3) the required equation in slope-interception form is:
y+16= -2x-6; ⇒ y= -2x-22.
note, the provided solution is not the only and shortest way.
Help ASAP! (20 points)
What is the slope-intercept equation for the following line?
y=__x+__
Answers
y = 2x + 7
m = slope = rise / run
m is found by using one random point and seeing how far up the next point is vertically (rise) and horizontally (run). In this case 2/1 which is just 2
And b = y-intercept, where the line touches the y-axis. In this graph it happens at 7
if the diagonal of a square is 11.3 what is the perimeter
Answers
Answer:
Step-by-step explanation:
if the diagonal of a square is 11.3 what is the perimeter
from the diagonal we find the area, which can also be found by multiplying diagonal by diagonal divided by two, then we make the square root of the area and find the side, we multiply by four and we have the perimeter
(11.3 * 11.3) : 2 = 63.8 u² (Area)
√63.8 = 7.9 (side)
7.9 * 4 = 31.6u (perimeter)
In Freeport, Illinois, Empire Street runs east to west and route 26 runs north to south.
Zippy’s Pizza parlor is located on route 26, 3 miles south of Empire street.
Zippy’s advertises that it delivers within a 4 mile radius.
Write an equation that represents the radius of delivery for Zippy’s Pizza. Assume that Zippy’s is located at the origin.
- How far east and west from route 26 can you live on Empire street and still receive Zippy’s Pizza delivery?
- Little Cubs Field is located 2 miles west and 4 miles north of Zippy’s. How far is Little Cubs Field from Zippy’s?
- How far is Little Cubs Field from the radius of delivery?
Answers
The area to which Zippy's Pizza makes delivery is 16·π square miles
The responses are;
First Part: x² + y² = 4²Second Part: √5 miles east and √5 miles west from route 26Third Part: 2·√5 milesFourth Part: 2·(√5 - 2) milesReasons:
The radius of the area that Zippy delivers pizza = 4 miles
Direction in which Empire Street runs = East to west
Direction of the route 26 route = North to south
Location of Zippy's Pizza parlor = 3 miles south of Empire street
-First Part:
The equation that represents the radius of delivery for Zippy's Pizza is given by the equation of a circle as follows;
(x - h)²+ (y - k) = r²
Where:
(h, k) = The center of the circle which is the location of Zippy's Pizza
r = The radius of the circle
Zippy's Pizza is at the center of the circular area with coordinates (h, k) = (0, 0)
r = 4 miles
-Which gives;
(x - 0)² + (y - 0)² = 4²
The equation that represent the radius is; x² + y² = 4²
-Second part:
The locations of addresses on Empire street, relative to Zippy's Pizza are given by the equation;
y = 3
Therefore, we have;
The furthest distances east and west on Empire street that can receive Zippy's Pizza delivery are given by the equation;
x² + 3² = 4²
x = √(4² - 3²) = ±√5
The furthest distances that can receive Zippy's Pizza delivery are ±√5 miles (east and west) from route 26
-Third Part:
Location of Little Cubs = 2 miles west and 4 miles north of Zippy's
The distance from Little Cubs Field to Zippy's = √((2² + 4²) = 2·√5
The distance from Little Cubs Field to Zippy's = 2·√5 miles
-Fourth Part:
The distance between Little Cubs Field from Zippy's radius of delivery, d, is found as follows;
d = 2·√5 - 4 = 2·(√5 - 2)
Therefore, d = 2·(√5 - 2) miles
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11. Consumer Math A store has apples on sale at $3.00 for 2 pounds.
a. How many pounds of apples can you buy for $9. Explain your answer
Answers
Answer:
6 pounds
Step-by-step explanation:
3$ for 2 pounds
9$ has three 3$
9 ÷ 3 = 3
Then multiply it to 2 pounds.
3 x 2 = 6
That's how we get the 6 pounds.
If the area of rectangle is x^2+5x+6, what expressions represent the length and width of the rectangle?
Answers
Answer:
length = x + 3
width = x + 2
Step-by-step explanation:
Hope it helps:)
what is 1 1/5 x 2 3/4
Answers
33
10
33
10
Decimal Form:
3.3
3.3
Mixed Number Form:
3
3
10
I hope it help #carry on learning
Step by step:
11(23)/5(4) (multiply 11 and 23)
253/5(4) (multiply 5 and 4)
=253/20
The grocery store carries diapers for children. Each diaper container has 48 diapers. Two dozen babies each need a container of diapers. How many diapers are needed?
Answers
Answer:
A 1152 diapers
Step-by-step explanation:
2dozen is 24, so 24×48=1152
each container= 48 diapers
2 dozen babies
to find:the amount of diapers needed
solution:[tex]12 \times 2[/tex]
[tex] = 24[/tex]
[tex]24 \times 48[/tex]
[tex] = 1152[/tex]
hence, 1152 diapers are needed for 2 dozen of babies.
answer= option A
whats the decimal equivalent of 16%
Answers
Answer:
0.16
Step-by-step explanation:
Percent means 'per 100'. So, 16% means 16 per 100 or simply 16/100.
The answer is 0.16
Answer:
0.16
Step-by-step explanation:
What is the slope of a line that passes through the points (4, - 3) and (- 2, 9)
Answers
Answer:
-2
Step-by-step explanation:
slope = y2 - y1 / x2 - x1
= 9 - (-3) / -2 -4
= 12 / -6
= -2
(simplify)
i will give brainliest if correct
28 ÷ 7 - √9
Answers
Answer:
The answer is 1
Step-by-step explanation:
28:7=4
√9=3
4-3=1
Answer:
1
Step-by-step explanation:
Square root of 9=3
28/7= 4
So 4-3=1
Answer is 1
Hope it is correct
Brian drove 638 miles in 11 hours.
At the same rate, how long would it take him to drive 754 miles?
Answers
Answer: 638 x= 754*11
638 x= 8294 then divide by both sides by 638
x = 13
she will drive 754 miles in 13 hrs.
Step-by-step explanation:
brainliest me
Find the value by using the suitable identities 84 2 The 2 is square so the question is 84 square Pls i need the ans fastt
Answers
84²
it is like saying 84×84
so
84×84=7,056
so our answer is
= 7,056
It takes Billy 40 minutes to drive to his friends house at his normal speed but it takes two hours if he drives 20 mph slower how far away is Billy's friends house
Answers
Answer:
Step-by-step explanation:
d/t=mph
Billy's friend's house is 20 miles away from him.
What is Speed?
The ratio of the distance travelled by an object to the time required to travel that distance.
Given that when Billy moves with his normal speed, it takes 40 min for him to reach his friend's house and if he slows his speed to 20 mph he takes 2 hours to reach the same distance.
We know, Speed = Distance/time
Let x be Billy's normal speed,
Therefore, 2x/3 = 2 (x - 20)
2x/3 = 2x - 40
x = 3x - 60
x = 30
Therefore, Billy's normal speed is 30 mph
Distance covered by him = 2 (30 - 20) = 20 mi
Hence, Billy's friend's house is 20 mi far.
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b/4 + 2 = -1
Please help, I’ll give brainliest to whoever answers correct first.
Answers
Answer:
[tex]\frac{b}{4}+2=-1[/tex]
Subtract 2 from both sides:
[tex]\frac{b}{4}+2-2=-1-2[/tex]
[tex]\frac{b}{4}=-3[/tex]
Multiply 4 to both sides:
[tex]4*\frac{b}{4} =-3*4[/tex]
[tex]b=-12[/tex]
Helpppppppppp please
Answers
Answer:
20 million
Step-by-step explanation:
Answer:
C twenty million
Step-by-step explanation:
Round the 2 populations to the nearest million.
The population of California is about 38 million.
The population of Texas is about 20 million.
The difference is 18 million.
The closest choice is 20 million.
Answer: C twenty million
Solve the simultaneous equations
3x - y = 5
-x + y = -1
Answers
Answer:
x= 2, y= 1
Step-by-step explanation:
3x -y= 5 -----(1)
-x +y= -1 -----(2)
(1) +(2):
3x -y -x +y= 5 -1
2x= 4
Divide both sides by 2:
x= 4 ÷2
x= 2
Substitute x= 2 into (2):
-2 +y= -1
y= -1 +2
y= 1
ticket sales for a local concert totaled $101,244 yesterday. After the ticket window closed today, the cashiers counted 968 tickets sold with a two-day total of $143,836. What is the cost of one concert ticket?
Answers
The cost of one concert ticket is approximately $148.59.
The tickets sales for the local sales is totalled $101, 244 yesterday.
ticket sales yesterday = $101244
He sold 968 tickets with a two-days total of $143, 836 (both yesterday and today)
The cost of one ticket can be calculated below:
cost of one ticket = 143,836 / 968
cost of one ticket = 148.590909091
cost of one ticket ≈ $ 148.59
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20 points
Please help me with these questions I am being timed
Answer the picture ones too please
Simplify:
(-8 + 35) + |-16 + 4|
Answers
Answer:
do I need to answer the questions in every pic?
Answer:
open the ones in bracket first
(_6)2 = _ 36
Step-by-step explanation:
so there fore 26.08 + (- 36) + 3.4 - 8.9 ÷ 9
open bracket by multiplying the signs
which implies
26.08 - 36 + (3.4 - 8.9) ÷ 9
- 9 .92 + (- 5.5) ÷ 9
open brackets by multiplying the signs
-9.92 - 5.5 ÷ 9
- 15.42 ÷ 9
which will give -1.713 approximately
find the slope and write the equation of the line that passes through the given points (5,6) and (3, 4)
Answers
Answer:
y=X +1
……. M=1
How do I answer this question?
Answers
Yan po correct me if im wrong po.. Salamat po...
What is 0.4184 in standard form
Answers
Answer:4.184*10^-1
Step-by-step explanation: in standard form or scientific notation
PLEASE HELP!! Which grabh does NOT represent a function?
Α) Α
B) B
C) С
D) D
Answers
Answer:
The answer is B!
Step-by-step explanation:
Using the vertical line test, two points meet while up and down. It'd be B.
in the inequality 4> -4 which number appears farther right on a number line and why?
Answers
Answer:
4
Step-by-step explanation:
It is a positive number meanwhile -4 in negative.
WILL MARK BRAINLIEST Evaluate (8xy³- 2x²- 3x + 1) ÷ (x - 1) WITH SOLUTION
Answers
Answer:
Given:f(x)=2x^2-3x-1
Then,f(-1)=2(-1)^2-3(-1)-1
f(-1)=2(1)+3-1
f(-1)=5-1
f(-1)=4
Step-by-step explanation:
Q1
Put these decimals in order, least to greatest:
?
0.11 0.3 0.12 0.2
Answers
Answer:
0.2,0.3,0.11,0.12
hope that helps
Answer:
0.11, 0.12, 0.2, 0.3
Step-by-step explanation:
Since the numbers are decimals, you can add as many zeros to the end of the numbers to make it easier. In this problem, add a zero to the end of 0.2 and 0.3, making them 0.20 and 0.30. This should make it easier. When you list the decimals from least to greatest, you should get 0.11, 0.12, 0.2, 0.3
I hope this helps!
What number is 32% of 75? Type a numerical answer in the space provided. Do not type spaces in your answer.
Answers
Answer:
24
Step-by-step explanation:
75 x .32 = 24
Answer:
32 percent of 75 is 24
Which represents the solution set of 5(x+5) <85?
X<12
Χ> 12
X< 16
Χ<16
Answers
Answer:
[tex]x<12[/tex]
Step-by-step explanation:
[tex]5(x+5)<85\\\\5x+25<85\\\\5x<60\\\\x<12[/tex]
Option A is correct, x<12 represents the solution set of 5(x+5) <85
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is 5(x+5) <85
We have to find the solution set of the given inequality
Five times of x plus five less than eight five.
Apply distributive property
5x+25<85
Subtract 25 from both sides
5x<85-25
5x<60
Divide both sides by 5
x<12
Hence, option A is correct, x<12 represents the solution set of 5(x+5) <85
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An equation is shown below:
4(x − 3) − 5(x + 1) = 3
Which statement shows a correct next step in solving the equation? (1 point)
Group of answer choices
The equation can become 4x − 12 − 5x − 5 = 3 by applying the associative property of multiplication.
The equation can become 4x − 3 − 5x + 1 = 3 by applying the associative property of multiplication.
The equation can become 4x − 3 − 5x + 1 = 3 by applying the distributive property.
The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.
Answers
Answer:
The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.
Step-by-step explanation:
4(x − 3) − 5(x + 1) = 3
The first thing would be distribute the 4 and the 5 respectively
4x-12 -5x-5 =3