If z = 1 –StartRoot 3 EndRoot i, what is z^3? please help im stressed


a) -8

b) 8

c) -8i

d) 8i

Answers

Answer 1

Answer:

Correct answer: a) -8

Step-by-step explanation:

Complex Numbers

A complex number z in polar form is expressed as

[tex]z=r(\cos\theta+\mathbf{i}\sin\theta)[/tex]

The nth power of a complex number in polar form is:

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

If the complex number is given in rectangular form

[tex]z=x+\mathbf{i}y[/tex]

then the values of r and θ are given by:

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

[tex]\displaystyle \theta=\arctan\left(\frac{y}{x}\right)[/tex]

The given complex number is:

[tex]z=1-\mathbf{i}\sqrt{3}[/tex]

The value of r is:

[tex]r=\sqrt{1^2+(-\sqrt{3})^2}[/tex]

[tex]r=\sqrt{1+3}=2[/tex]

r=2

Calculating the angle:

[tex]\displaystyle \theta=\arctan\left(\frac{-\sqrt{3}}{1}\right)[/tex]

[tex]\displaystyle \theta=\arctan(-\sqrt{3})[/tex]

Since the number is in the quadrant IV, the angle is:

[tex]\theta=-60^\circ[/tex]

Thus, z is expressed in polar form as:

[tex]z=2(\cos(-60^\circ)+\mathbf{i}\sin(-60^\circ))[/tex]

Calculating:

[tex]z^3=2^3(\cos(-180^\circ)+\mathbf{i}\sin(-180^\circ))[/tex]

Given cos 180°=-1 and sin(-180°)=0

[tex]z^3=8(-1+0)[/tex]

[tex]z^3=-8[/tex]

Correct answer: a) -8

Answer 2

Answer:

A

Step-by-step explanation:

just finished test


Related Questions

What is the greatest common factor of 10 and 16? Then, use the greatest common factor to write an equivalent expression of 10 + 16.

Answers

Answer:

GCF is 2

Step-by-step explanation:

10+2+16

math 6th grade
Suppose an artist is working on a painting. On Monday, he painted 1/2 of it. On Tuesday, he completed another 1/3 of the painting. What percent of the painting has yet to be done? Round your answer to the nearest whole percent.

Answers

Answer:

17%

Step-by-step explanation:

1/2+1/3=5/6,so 1/6 left. That is 16.66666666666667 or 17%..

Hope this helps plz hit the crown :D

Which expression is not equivalent to the other three A) -9- 7 + 16n

Answers

Answer:

-16(1-n)

Step-by-step explanation:

Answer:

your answer would be -16(1-n)

Step-by-step explanation:

Consider the equation 0.16m - 0.4 - 0.4 what is the value of m?
A. 0
B. 2.1
C. 2.9
D. 5

Answers

Answer: I think it’s 5

Step-by-step explanation:

Well if you go on calculator 16 * 5 which would represent m - 0.4 would give you the answer 0.4.

please solve this question

Answers

Answer:

the answer is b

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Both of the cost for 8 hours is $30

Can someone show me how do I do this please?

Answers

Answer:

the awnser is c

Step-by-step explanation:

A- 100:1 would mean it is a 10000% markup

B- 1:100 lower than b so eliminate

C- 2:1 So a is double the amount of b so it's 100%

D- 1:2 B is 100% of a so it's flipped, not what question is asking for

So process of elimination shows that C is the correct awnser

noah has d dimes and q quarters. he has no less than 17 coins altogether. write this situation as an inequality​

Answers

Answer: d + q  > 17

Step-by-step explanation:

Jenna is making 9 costumes for the dance recital. Each costume uses 12 feet of fabric. How much fabric does Jenna need altogether? Use distributive property to solve.

Answers

Answer:

108

Step-by-step explanation:

If there is 9 costumes and each of the 9 costumes is 12 feet then you multiply 9 x 12 to get the answer, which is 108. (Please give me brainliest)


In the figure below, m show work i’ll make you brainliest plz help

Answers

We need the picture to answer so if you could take a picture and put it on the question

A passenger train travels 528 miles in 8 hours

Answers

Answer:

66 miles per hour

Step-by-step explanation:

528/8 = 66 miles per hour

Answer:

66 miles/hour.

Step-by-step explanation:

Its average speed is 528/8

= 66 miles/hour.

Please help me answer please

Answers

Answer:

x=75

Step-by-step explanation:

I'm lost at this point, if you can help me I'll give you 10 points..

Answers

Answer:

So all the possible solutions are:

[tex]\bold{204.4~and~217.6.}[/tex]

Solution Steps:

First you need to solve the real inequality to understand how to find the rest of the possible equations.

Subtract 13.2 from both sides:

[tex]13.2-13.2=[/tex] Cancels Out[tex]217.6-13.2=204.4[/tex]

So now we know the real answer, but now we must find all the possible solutions.

(Means anything greater than or equal to 217.6 when you plug it into x + 13.2 ≥ 217.6.)

Numbers that are greater than 378:

  1.)  [tex]204.4+13.2=217.6[/tex] ≥ [tex]217.6[/tex]  (True)

  2.)  [tex]217.6+13.2=230.8[/tex] ≥ [tex]217.6[/tex]  (True)

  3.)  [tex]204.3+13.2=217.5[/tex] ≥ [tex]217.6[/tex]  (False)

  4.)  [tex]0+13.2=13.2[/tex] ≥ [tex]217.6[/tex]  (False)

  5.)  [tex]13.2+13.2=26.4[/tex] ≥ [tex]217.6[/tex]  (False)

  6.)  [tex]200.4+13.2=213.6[/tex] ≥ [tex]217.6[/tex]  (False)

  7.)  [tex]-200+13.2=-186.8[/tex] ≥ [tex]217.6[/tex]  (False)

  8.)  [tex]13.2+13.2=26.4[/tex] ≥ [tex]217.6[/tex] (False)

Now put all the numbers together to form the code.

(Could either be the numbers on the side of the table or the accumulation of all the numbers in possible solutions.)

Code:

[tex]2044,2176[/tex] or [tex]1,2[/tex]

______________________________

 [tex]\bold{Hope~this~helps!}\\\bold{If~you~need~help~with~anything~else,~feel~free~to~ask!}\\\\\bold{~~~~~-TotallyNotTrillex}[/tex]

Three friends grow groups of sunflowers.
Some think that Anna’s flowers are the tallest because the mean height of her flowers is the greatest.
Others think Anna’s flowers are the shortest because the median height of her flowers is the least.

The plots show the heights for each friend’s flowers.

Which is the most likely plot for Anna’s flowers?

Answers

Step-by-step explanation:

es la numero     3

Answer:

Option 3 is the most common plot for Anna’s flowers

Simplify the expression by combining like
terms:
2m2 - m + 4m2 + 8m
Enter the number that belongs in the green box.
[?]m2 + []m

Answers

Answer:

Step-by-step explanation:

2m^2-m+4m^2+8m combine like terms

6m^2+7m

Answer:

15m

Step-by-step explanation:

2m²-m+4m+8m

2m•2m-m+4m+8m

4m-m+4m+8m

3m+12m

15m

please help!! <3 and plsexplain how u got it *15 points*
Kiyo bought a pizza for $12.75 and four medium drinks at Pauli's Pizza. Define a variable and write an expression to represent the total amount of money he spent. Then find the total cost if one drink costs $3.

Answers

Answer:

4×3=12 total cost for the drinks

12.75 + 12= $24.75 total cost for the pizza and drinks combined

The following graphs show the performance of two stocks over the first five months of the year. A graph titled Stock A B C has month on the x-axis, from 0 to 6, and price on the y-axis, from 0 to 40 in increments of 13.33. A line has points (1, 20), (2, 24), (3, 25), (4, 29), (5, 30). A graph titled Stock X Y Z has month on the x-axis, from 0 to 6, and price on the y-axis, from 20 to 32 in increments of 4. A line has points (1, 20), (2, 24), (3, 25), (4, 29), (5, 30). Which graph appears to show the best performance? Which scale makes the graph appear to be rising more slowly? a. Stock XYZ shows the best performance. The scale of Stock ABC makes the graph appear to be rising more slowly. b. Stock ABC shows the best performance. The scale of Stock ABC makes the graph appear to be rising more slowly. c. Stock XYZ shows the best performance. The scale of Stock XYZ makes the graph appear to be rising more slowly. d. Stock ABC shows the best performance. The scale of Stock XYZ makes the graph appear to be rising more slowly.

Answers

Answer:

C) Stock XYZ shows the best performance. The scale of Stock XYZ makes the graph appear to be rising more slowly.

Step-by-step explanation:

i did this question on my test, from reading the graph, i am almost certain this is the answer. correct me if i am wrong!

Answer:

B)

Step-by-step explanation:

B because the  Stock XYZ shows the best performance. The scale of Stock ABC makes the graph appear to be rising more slowly.

Find the distance between points p (-2,6) and q (4,-8)

Answers

Answer: 2√58

the distance between points p (-2,6) and q (4,-8) is [tex]\sqrt{(4-(-2))^{2}+(-8-6)^{2} } =\sqrt{6^{2} +(-14)^{2} }=2\sqrt{58}[/tex]

Step-by-step explanation:

Write the slope intercept form of the equation of the line through the given points.
through: (0, 2) and (-4, -1)

Answers

Answer:

You use the formula (y to the second power minus y to the first power minus the same formula with the two different points

Step-by-step explanation:

Simplify the expression
(-a)^-18

Answers

Answer: it is the first option in the photo so A

A little girl counts using the fingers of her left hand as follows: She starts by calling her thumb 1, the first finger 2, middle finder 3, ring finger 4, and little finger 5. Then she reverses direction, calling the ring finger 6, middle finger 7, first finger 8 and thumb 9, after which she calls her first finger 10 and so on. If she continues to count in this manner, on which finger will she stop?
a) What if the girl counts from 1 to 10?
b) What if the girl counts from 1 to 100?
c) What if the girl counts from 1 to 1000?

Answers

Answer:

(a) Index finger

(b) Ring finger

(c) Index finger

Step-by-step explanation:

Taking thumb as standard for the question.

Thumb series 1 , 9 , 17 ,25, 33......

general term for this

a(n) = 1 + (n-1)8

      = 1 + 8n -8

       = 8n -7

(a) For 1 to 10

     8n -7 = 10

     8n = 16+1 (remainder)

so the thumb is for 9 and the next is index finger.

10th = index finger.

(b) for 1 to 100

    8n - 7 = 100

      8n= 107

     107 = 13x 8 + 3(remainder)

so the third finger from thumb is Ring finger

100th = Ring finger

(c) 8n - 7 = 1000

   8n = 1007      

 1007= 125x8 +7 (remainder)

so the 7th finger next to thumb is Index finger

1000th = index finger

Please help me out :)

Answers

1. D
2.B
3.A
4. D i think i can’t really see that question
5.C

Divide. Write your answer as a fraction or mixed number in simplest form.

8 • 3 3/5

Answers

The answer is 2 wholes and 2 nineths

Subtract 0.6 - 0.23.

Answers

0.37 that’s the answer have a good day

What is the scale factor of this dilation?
1/2
3/5
1 2/3
2
Helpppppp plz I’ll give brainliest if it’s right.

Answers

The answer is 3/5 because i did the math on my paper and yea

This question is based on Algebra 1
solve for X

3x-4y=7

Answers

Answer:

[tex]x=\frac{4y+7}{3}[/tex]

General Formulas and Concepts:

Alg I

Equality Properties

Step-by-step explanation:

Step 1: Define

3x - 4y = 7

Step 2: Solve for x

Add 4y to both sides:          3x = 4y + 7Divide 3 on both sides:        x = (4y + 7)/3

Tyler ate x fruit snacks, and Han ate 34 less than that. Write an expression for the number of fruit snacks Han ate.

Answers

Answer:

x = -3/4

Step-by-step explanation:

Because you have the variable x and you do not know the number of fruit snacks he ate and you need to have the same variables to properly find the answer.

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Given that f(x)=4x3-12x2+10 and g(x)=x3 – 2x2 + 5x
The value of f(x)- g(x)= ax'+bx?+ cx+d. What are the values of the coefficients a,b,c,d?

Answers

Answer:

The values of a,b,c and d are as follows:

a = 3, b = -12, c = -5, d = 10

Step-by-step explanation:

Given functions are:

[tex]f(x) = 4x^3-12x^2+10\\g(x) = x^3-2x^2+5x[/tex]

We have to find the value of f(x) - g(x). This means we have to subtract function g(x) from function f(x)

So,

[tex]f(x) - g(x) = (4x^3-12x^2+10)-(x^3-2x^2+5x)\\= 4x^3-12x^2+10-x^3+2x^2-5x[/tex]

Combining alike terms

[tex]= 4x^3-x^3-12x^2+2x^2-5x+10\\= 3x^3-10x^2-5x+10[/tex]

Now it was given that:

f(x)- g(x)= ax^3+bx^2+ cx+d

By comparing both we get

a = 3, b = -12, c = -5, d = 10

Hence,

The values of a,b,c and d are as follows:

a = 3, b = -12, c = -5, d = 10

please help anyone ​

Answers

Answer:

p = 30

Step-by-step explanation:

EFGH is a cyclic quadrilateral ( all vertices lie on a circle )

The opposite angles of a cyclic quadrilateral are supplementary, thus

p + 5p = 180

6p = 180 ( divide both sides by 6 )

p = 30

Salma and John walk around a track. Salma walks each lap in 10 minutes. John walks each lap in 12 minutes. The two of them begin at the starting line at the
same time. They walk until they meet again at the starting line.

Answers

Answer:

If you're asking how long it will take for them to meet again, it will take 60 minutes.

Step-by-step explanation:

Find GJ
27
Please it’s due in one hour please please anyone

Answers

Answer:

the answer is 27 because hg is the same length as gj

It would have to be 27 because the side GH is the same as GJ.

Hope this helped!

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