Mathematics College

Given the complex number z=6(cos120+isin120), find z3

Given The Complex Number Z=6(cos120+isin120), Find Z3

Answers

Answer 1

Answer:

B

Step-by-step explanation:

We are given the complex number:

[tex]\displaystyle z = 6(\cos 120^\circ + i\sin 120^\circ)[/tex]

And we want to find z³.

Recall that:

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

In this case, n = 3. Hence:

[tex]\displaystyle z ^3 = (6)^3 (\cos (3(120^\circ)) + i\sin (3(120^\circ))[/tex]

Simplify:

[tex]\displaystyle z^3 = 216(\cos 360^\circ + i\sin 360^\circ)[/tex]

Evaluate:

[tex]\displaysyle z^3 = 216( 1 + i(0)) = 216[/tex]

In conclusion, our answer is B.

Related Questions

Theodore invests a total of $19,500 in two accounts paying 8% and 15% simple interest, respectively. How much was invested in each account if, after one year, the total interest was $2,400.00
A) Enter an equation that uses the information as it is given that can be used to solve this problem. Use x as your variable to represent the amount of money invested in the account paying 8% simple interest.

Answers

Answer:

[tex]x+y=19500,\:0.08x+0.15y=2400\quad :\quad x=7500,\:y=12000[/tex]

Step-by-step explanation:

x + y = 19500

.08x + .15y = 2400

* 1. Find the two roots X7 and x2 of the quadratic equation x2 – 8x + 12 = 0. Enter y

Answers

9514 1404 393

Answer:

  x = 2, x = 6

Step-by-step explanation:

The quadratic can be factored as ...

  x^2 -8x +12 = 0

  (x -2)(x -6) = 0

Solutions are the values of x that make these factors zero:

  x -2 = 0   ⇒   x = 2

  x -6 = 0   ⇒   x = 6

plot function f on the graph f(x) = |1/2x - 2|​

Answers

Answer:

See attached

Step-by-step explanation:

Given function:

f(x) = |1/2x - 2|​

The function is plotted and it is below.

The graph of the function f(x) = | (x/2) - 2 | is attached with the answer the lines of the function meet at point 4 at the x-axis.

What is a graph?

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The graph of the function f(x) = | (x/2) - 2 | is attached with the answer the lines of the function meet at point 4 at the x-axis.

Therefore graph of the function f(x) = | (x/2) - 2 | is attached with the answer the lines of the function meet at point 4 at the x-axis.

To know more about graphs follow

https://brainly.com/question/25020119

#SPJ2

simplify 3√578 - √162 + 4√32

Answers

[tex]3\sqrt{578}-\sqrt{162}+4\sqrt{32}=\\\\=3\sqrt{289\cdot2}-\sqrt{81\cdot2}+4\sqrt{16\cdot2}=\\\\=3\sqrt{17^2\cdot2}-\sqrt{9^2\cdot2}+4\sqrt{4^2\cdot2}=\\\\=3\cdot17\sqrt2-9\sqrt2+4\cdot4\sqrt2=\\\\=51\sqrt2-9\sqrt2+16\sqrt2=51\sqrt2+7\sqrt2=\boxed{58\sqrt2}[/tex]

Name the angle in three different ways

Answers

Answer:

angle WVU

angle UVW

angle VUW

Step-by-step explanation:

Write the answer without using exponents? -9^3

Answers

Answer:

1/729

Step-by-step explanation:

a negative exponent is fractioned like 1/9^3. Which can be simplified as 1/729 ans 9^3 = 729

At the gift shop they sell small grettong card and large greeting cards. The cost of small ones are 1.80 and the cost of large ones are 4.40. How much does it cost to get 5 small ones

Answers

Answer:

$9

Step-by-step explanation:

Since the question only asks for small ones, we only need to focus on 1.80 and 5. Multiple them. 1.80×5 and we get 9. 1.80×5=9

Write 2100 in scientific notation.

Answers

2.1 x 10 to the third power
There hope that helps

What is the LCM of 42 and 63?

Please show work! I'm very confused and don't understand.

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\rm{LCM\ (aka\ Lowest\ Common\ Multiple)\ is\ the}}\\\huge\boxed{\rm{lowest\ positive \ number\ has \ a \ multiple}}}\\\huge\boxed{\rm{of\ more\ than\ one\ number.}}[/tex]

[tex]\huge\boxed{\rm{The\ multiples\ of\ 42\ are: 42, 84, 126, 168, \& \ 210}}[/tex][tex]\huge\boxed{\rm{The \ multiples \ of \ 63\ are: 63, 126, 189, \& \ 252}}[/tex]

[tex]\huge\boxed{\rm{Therefore, your\ answer\ is: 126}}}[/tex]

[tex]\huge\boxed{\text{Good luck on your assignment \& enjoy your day,}}[/tex]

~[tex]\huge\text{Amphitrite1040:)}[/tex]

One number is 7 more then the other and their sum is 17

Answers

Answer:

Let the unknown number be x and the other greater number be x+7

(x+7)+x=17

2x=17-7

x=5

x+7=5+7

     =12

Given the following function:

()=−2+2

Answers

Answer:

0...................

Step-by-step explanation:

0

Give the slope and the y-intercept of the line y=9x+7 . Make sure the y-intercept is written as a coordinate.

Answers

Answer:

The slope is 9

The y intercept is (0,7)

Step-by-step explanation:

y=9x+7

The equation is written in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 9

The y intercept is (0,7)

baseand power : (-4(−4/8)²​

Answers

300000000030000000030000

for each function, what is the output of the given input?
For f(x) = -5x +1, find f(3).

a. -16
b. -14
c. -2
d. 16

Answers

Answer:

b. -14

Step-by-step explanation:

x is now 3

so -5(3)+1 = -14

Fjjfnd djdndjdnndnddn dndnxndn

Answers

Answer:

C. angle 7

Step-by-step explanation:

...............

should be letter c :))

WILL GIVE BRAINLEST
Slove f(-4) if f(x) = -4x -2
Give Step by Step pls.

Answers

Answer:

Use the given functions to set up and simplify f(−4).

14

Step-by-step explanation:

Plug x + h into the function f and simplify to find f(x + h). Now that you have f(x + h), find f(x + h) - f(x) by plugging in f(x + h) and f(x) and simplifying. Plug your result from step 2 in for the numerator in the difference quotient and simplify.

https://study.com/academy/lesson/how-to-solve-the-difference-quotient.html

Dose anyone know how to solve this?

Answers

Answer:

Derivative of any constant is zero

you can solve it by first derivative rule

Answer:

Derivative of any constant is zero

Step-by-step explanation:

there were 450 balloons in all a total of 60% were used to how many were used​

Answers

Let used balloon be x

[tex]\\ \sf\longmapsto x=60\%\:of\:450[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{60}{100}\times 450[/tex]

[tex]\\ \sf\longmapsto x=45(6)[/tex]

[tex]\\ \sf\longmapsto x=270[/tex]

Step-by-step explanation:

Solution,

Let the number of used balloons be x,

Given:-

Total number of balloons= 450Used percentage of balloons= 60%

Now,

Number of used balloons(x)=

60% of 45060/100×450270

Hence, 270 balloons were used.

Divide. Write your answer as a fraction or a mixed number in simplest form.
3 1
9- : 4
4 2

Answers

Answer:

2 4/25 hope that helped

Step-by-step explanation:

Help asap plz first answer get brainliest

Answers

Answer:

Use a mixed fractional calculator. No one is gonna help u with this many questions...

https://www.calculatorsoup.com/calculators/math/mixednumbers.php

GL

Step-by-step explanation:

Understanding Square and Cube Roots - Item 31415
Ques
Drag numbers to complete the table for missing values of x. x and x?.
LEER
25
3
27
81
15
19
х
*2
23
9
DRAG AND DROP
• AN ITEM HERE
DRAG AND DROP
AN ITEM HERE
125
5
DRAG AND DROP
AN ITEM HERE

Answers

Answer:First: 3Second: 25Third: 81Hope this helps!! <3 :)

3p squared + 6p + 18 divided by p - 6

Answers

9514 1404 393

Answer:

  3p +24 +162/(p-6)

Step-by-step explanation:

The result of the division can be found using polynomial long division, or using synthetic division. The latter requires less writing and gives the same answer:

  [tex]\dfrac{3p^2+6p+18}{p-6}=3p+24+\dfrac{162}{p-6}[/tex]

An investment of $500 earns $70 simple interest after 6 years. To the
nearest tenth of a percent, what is the interest rate?

Answers

Answer:

Rate of interest is 2.3%

A regular hexagon is a six sided figure with all sides equal and all six angles equal. Find the length of the sides if the perimeter of the regular hexagon is 396 yd.

Answers

Answer:

sides = 61.5 yd

Step-by-step explanation:

hopefully the picture I have attached us clear and understandable

:)

An apple juice factory produced 6,425.51 gallons of apple juice in 4 days. How much apple juice, on average, did the factory produce each day? ​

Answers

6426.51/4 = one day
= 1,606.6275 gallons/day

The box office manager said about 5,000 people attended the show. Write a number that could be the actual attendance. If he correctly rounded to the nearest hundred

Answers

9514 1404 393

Answer:

  4983

Step-by-step explanation:

Your answer could be any value between 4950 and 5049, inclusive. Below 4950 rounds down; 5050 and above rounds up.

A 4" by 6" by 8" rectangular solid is cut by slicing through the midpoint of three adjacent edges. What is the number of inches in the sum of the lengths of the edges of the tetrahedron that is cut?

Answers

Answer:

22.078

Step-by-step explanation:

I have attached the images above

Find the distance between the points
AC-3, 2) and B (5,7) to the nearest
hundredth.

Answers

Answer:

Step-by-step explanation:

d=[tex]\sqrt{(5+3)^{2} +(7-2)^{2} }[/tex]

 =[tex]\sqrt{(8)^{2}+(5)^{2}}[/tex]

 =[tex]\sqrt{64+25}[/tex]

 =[tex]\sqrt{89}[/tex]

Solve 7x- c= k for x.
O A. x = 7(k-c)
O B. x =
*=***
O C. x = 7(k+ C)
K-c
O D. X=
7
- KM

Answers

the answer is in the photo

Mia cuts up a piece of wood 4 1/2m long into pieces measuring 3/4m long. How many pieces are there?

Answers

Answer:

6

Step-by-step explanation:

to find how many pieces we use division

we divide the main piece of wood size ÷ small sizes

4.5 ÷0.75 = 6 pieces

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