If z = 1 + StartRoot 3 EndRooti, what is z5? 16 + 16StartRoot 3 EndRoot i –16 + 16StartRoot 3 EndRoot i –16 – 16StartRoot 3 EndRoot i 16 – 16StartRoot 3 EndRoot i

Answers

Answer 1

Answer:

The answer is C

Step-by-step explanation:

Correct answer shown on edge

Answer 2

The power of 5 of complex number z is (-16√3 + 16) + 4(-√3 + 3)i

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:

z = 1 + √3i

We have to find: z⁵

z⁵ = (1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)(1 + √3i)

z⁵ = (-2 + 2√3)(1 + √3i)(1 + √3i)(1 + √3i)

[tex]\rm z^5=\left(2\sqrt{3}-2\right)+2\left(3-\sqrt{3}\right)i(1+\sqrt{3}i)(1+\sqrt{3}i)[/tex]

[tex]\rm =\left(-4\sqrt{3}+4\right)+4\left(3-\sqrt{3}\right)i(1+\sqrt{3}i)[/tex]

z⁵ = (-16√3 + 16) + 4(-√3 + 3)i

Thus, the power of 5 of complex number z is (-16√3 + 16) + 4(-√3 + 3)i

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Related Questions

Which polynomial can be factored using the binomial theorem?

81x2 + 117x + 169
81x2 + 234x + 169
6,561x4 – 9,477x3 + 13,689x2 – 19,773x + 28,561
6,561x4 – 18,954x3 + 27,378x2 – 39,546x + 28,561

Answers

Answer:

B.) 81x2 + 234x + 169

Step-by-step explanation:

Twins Isaac and Isaiah were just born. Isaac weighs 6666 pounds 2222 ounces and Isaiah weighs 5555 pounds 4444 ounces.

Answers

Step-by-step explanation:

Kindly make the question clearer for assistance

make the question more clear pls

Someone please help! What is the domain and range of the relation?

Answers

Answer:

The domain is the set of all first elements of ordered pairs (x-coordinates).

The range is the set of all second elements of ordered pairs (y-coordinates).

Only the elements "used" by the relation or function constitute the range.

What would you tip for a $22 meal if you wanted to leave 15%?
$18.70
$4.40
$3.30
$25.30

Answers

3.30 because 22 x 15% = 3.3
3.30,good luck with your math

plx help i need to get this so I can be ungrounded ​

Answers

Answer:

2

Step-by-step explanation:

I agree 2- why’d you get grounded

choir is selling Pringle chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches . Which equation can be used to find the volume of the container?
1,,,,,,,V=pi(9)
2,...... V=pi(9)^2(32)
3,........V=pi(4.5)^2(32)
4,........V=pi(4.5)(32)

Please does anyone know the answer?

Answers

Answer:it’s V=pi(4.5)^2(32)

Step-by-step explanation:

The equation which can be used to find the volume of the container of Choir who is selling Pringle chips, is

[tex]V=\pi (4.5)^2(32)[/tex]

What is of volume of cylinder?

Volume of cylinder is the amount of quantity, which is obtained by it in the 3 dimensional space.

Volume of cylinder is the can be given as,

[tex]V=\pi r^2h[/tex]

Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.

Choir is selling Pringle chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches.

As the radius is half of the diameter. Thus, the radius of the container is,

[tex]r=\dfrac{9}{2}\\r=4.5\rm\; in[/tex]

As this container is in the shape of cylinder. Thus, the volume of container can be found out using the above formula as,

[tex]V=\pi (4.5)^2(32)[/tex]

Hence, the equation which can be used to find the volume of the container of Choir who is selling Pringle chips, is

[tex]V=\pi (4.5)^2(32)[/tex]

Learn more about the volume of cylinder here;

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a man goes 10m due east and 24m due north find the distance from the starting(pls help )

Answers

Answer:

26m

Step-by-step explanation:

10^2+24^2=26^2

please help but right answers

Answers

Answer:

51=-3x+6 -6

45=-3x ÷(-3)

-15=x

Step-by-step explanation:

prove me wrong

Answer:

r=-15

Step-by-step explanation:

51-(-3r+6)=0

3r-6+51=0

3r+45=0

3r=-45

r=-45/3

r=-15

Can some one plz help i will give BRAINLIEST.

If there is a 10% chance of a certain flower species having blue petals, then is it possible to observe only 85 flowers with blue petals in a field of 1000 flowers? Explain your reasoning.

Answers

Answer:

Yes

Step-by-step explanation:

10% chance does not mean it is always 10 percent. 10 percent is the theoretical property. The experimental probability can be different than the theoretical property.

An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?

Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course). Use a significance level of α=0.1 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.

Student 1 2 3 4 5 6 7
Score on first SAT 500 380 560 430 450 360 560
Score on second SAT 540 470 580 450 480 400 600

Required:
a. State the null and alternative hypotheses for the test.
b. Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.
c. Compute the value of the test statistic. Round your answer to three decimal places.
d. Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to three decimal places.
e. Make the decision for the hypothesis test.

Answers

Answer:

Since the calculated value of t = -0.215  falls in the critical region so we accept Ha that SAT prep course improves the students' verbal SAT scores and reject the null hypothesis at significance level 0.05.

e. These results support the claim that the SAT prep course improves the students' verbal SAT scores.

Step-by-step explanation:

Student                        1      2      3       4      5         6          7

Score on first SAT    500   380 560   430  450    360    560

Score on second SAT 540 470 580  450    480    400    600

Difference d                -40  -90   -20    -20    -30     -40     -40     ∑ -280

d²                               1600  8100 400 400   900   1600  1600   ∑14600

a. Let the hypotheses be

H0:  ud= 0      against the claim Ha: ud ≠0

The degrees of freedom = n-1= 7-1= 6

The significance level is 0.05

The test statistic is

t= d`/sd/√n

The critical region is ║t║≤ t (0.025,6) = ±2.447

d`= ∑di/n= -280/7= -4

Sd²= ∑(di-d`)²/n-1 = 1/n-1 [∑di²- (∑di)²n]

= 1/6[14600-(-4)²/7] = [14600-2.2857/6]= 2432.952

b. Sd= 49.3249= 49.325

Therefore

c. t= d`/ sd/√n

t=   -4/ 49.325/√7

t= -4/18.6435 = -0.2145= -0.215

d. Since the calculated value of t = -0.215  falls in the critical region so we accept Ha that SAT prep course improves the students' verbal SAT scores and reject the null hypothesis at significance level 0.05

e. These results support the claim that the SAT prep course improves the students' verbal SAT scores.

A giant tortoise moves at a slow but steady pace. It takes
the giant tortoise 3 seconds to travel 10.5 inches.
How many inches will the tortoise travel in 1 second?

Answers

the answer should be that it will take the tortoise 1 second to travel 3.5 inches


The ratio using a colon is

Answers

a ratio?

What numbers a provided

How many groups of 3/4 are in each of the following quantities?


Type your response in each box below.


1. 11/4 has __

groups of 3/4.


2. 6 1/2 has ___

groups of 3/4.

Answers

Answer:

  vb\

Step-by-step explanation:

3d - 5+4d +5=140 how do i solve this i need help

Answers

Answer:

3

5

+

4

+

5

=

1

4

0

3d{\color{#c92786}{-5}}+4d+{\color{#c92786}{5}}=140

3d−5+4d+5=140

3

+

4

=

1

4

0

3d+4d=140

3d+4d=140

2

Combine like terms

3

+

4

=

1

4

0

{\color{#c92786}{3d}}+{\color{#c92786}{4d}}=140

3d+4d=140

7

=

1

4

0

{\color{#c92786}{7d}}=140

7d=140

3

Divide both sides of the equation by the same term

7

=

1

4

0

7d=140

7d=140

7

7

=

1

4

0

7

\frac{7d}{{\color{#c92786}{7}}}=\frac{140}{{\color{#c92786}{7}}}

77d​=7140​

4

Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

=

2

0

d=20

d=20

Solution

=

2

0

hope it help

Step-by-step explanation:

Answer:

the answer is 20

Step-by-step explanation: combine like terms

7d = 140

then divide

140/7

20

Answer all questions and the topic is about ordering decimals and don't answer if u do not know.

Answers

Answer:

31. 0.93, 0.9, 0.33

27. 6.13, 6.14, 6.31

28. 3.09, 3.19, 3.9

29. 12.96, 12.83, 12.8

25. 9.06, 9.6, 9.66

26. 0.09, 0.67, 0.86

Step-by-step exp

During a basketball game, the coach needs to select a player to make the free throw after a technical foul on the other team. There is a 68% chance that the coach will select you and a 26% chance that the coach will select your friend. What is the probability that you or your friend is selected to make the free throw?

Answers

For the probability of you or your friend add the probability of each together:

68% + 26% = 94%  (0.94 if you need it as a decimal)

Answer: there's an 42 percent chance that your friend might make a free throw.

Step-by-step explanation: if u subtract u will get your answer that's bow i got this answer.

A system of equations is shown on the graph below How many solutions does this system have?
no solutions
one unique solution
two solutions
an infinite number of solutions

Answers

Answer:

There is only one solution.

Step-by-step explanation:

The two lines only cross once, so there is one solution.

If the lines did not cross at all, there would be no solutions.

If the lines crossed twice, then there would be two solutions.

If the lines were on top of one another, they would be the same line, and have an infinite amount of solutions.

A system of equations is shown on the graph below has Unique solution.

What is Line segment?

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

The graph is shown in figure.

Now,

Since, In the graph the two line segment cut into one point.

Hence, The system of equation shown in graph has Unique solution.

Thus, A system of equations is shown on the graph below has Unique solution.

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(1/2(7x3))^3= plz help

Answers

Answer:

1/2 X 7 X 3 X 3 = 31.5

Step-by-step explanation:

At the end of school, Josh's teacher handed out 27 coupons for bowling during the summer to each student. The third week of
summer, he accidentally threw away 15 of them when he cleaned his room. The last week of summer, he decided to use the
remaining coupons evenly over 3 days.
If he did not use any of the coupons until the last week of summer, how many coupons did he use on each of the 3 days?

Answers

The answer would be 4 Coupons

I NEED HELP THIS IS DUE IN THIRTY MINUTES
convert decimals to fractions
1.167
2.4
1.75

Answers

Answer:

1167/1000

24/10

175/100

Step-by-step explanation:

1.167

we consider the point is equal to 1. After that point, all numbers, we consider as zero.

so, the answer would become:

1167/1000

Which of the following is a factor of x^4 - 5x^3 + 3x^2 + 15x - 2
A. 2x+3
B. x-3
C. 3x+1
D. Not factorable

Answers

Answer:

D. Not factorable

Step-by-step explanation:

The math clubs car can travel 9 meters in a second. The race track for the soap box derby is 63 meters long. How many seconds will it take the Math clubs car to make it around the track

Answers

Answer: it will take 7 seconds

Step-by-step explanation: 9 x 7 = 63

Which of these expressions equal 15 when x=1/2 and y=3? Circle all that apply. Please help with this my teacher need me to work out xy+3 1/2+20x Btw guys 3 1/2 are mixed numbers if your wondering

Answers

Answer:

15

Step-by-step explanation:

First you would replace the x and y's with 1/2 and 3.

So it would look like: (1/2) (3) + 3 1/2 + 20 (1/2)

Next, you go by PEMDAS (parenthesis, exponents, multiplications, division, addition, subtraction)

So you would first multiply and the parenthesis that I added mean multiplication.

1.5 + 3.5 + 10

So then all that is left to do is add because I multiplied everything out.

So it is 5 + 10 which is 15

What is 1/4 times 24.80

Answers

Answer:

6.2 is the answer you are looking for

Write an explicit formula for the sequence -13,-6,1,8, ...
A. an= -13n+7
B. an= -13+(n+7)
C. an= -13+7(n-1)
D. an= -13n+7

Answers

Answer:

7n-20 I believe

Step-by-step explanation:

hope this helps

Answer: A

lol need extra characters

i took the test btw

HELP PLS! ILL MARK BRAINLIEST!

Sean drink a slushy as fast as he could. The amount of Slushii left in a cup (in milliliters) as a function of time (in seconds) is graphed. How fast did Sean drink the slushy?

A. 8 mL per second
B. 0.8 mL per second
C. 1 mL per second
D. 10 mL per second

Answers

i think b sorry if it’s wrong :(

6) Which of the following angles is coterminal with -495 degrees?
45 degrees
135 degrees
225 degrees
315 degrees

Answers

Answer:

225 degrees

Step-by-step explanation:

-495 +360 until you get to one of the answers.

The side opposite from the right angle is called

Answers

Answer:

The side opposite from the right angle is called the hypotenuse.

Find the quotient: 8,358 ÷ 27 = ________.
309 r 15
309 r 26
310 r 15
310 r 26

Answers

Answer:

the answer is 309 r 15

Step-by-step explanation:

309 × 27 is 8343 and your left with 15


This trip the family will spend $117.96. The next trip they will spend $119.27. This is an increase of ($117.96 − $119.27) or an increase of $1.31.

What is the percent of increase?

Round your answer to the nearest whole percent. Type your answer into the space.

Answers

Answer:

1.11055% increase

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