If Z= 2+2i, what is z^4?

Answers

Answer 1

Answer:

D. 64 (cos(pi)+isin(pi))

Step-by-step explanation:

Put 2+2i into trigonometric form, raise the r value to the power of 4, and multiply the angle value (theta) by 4 to get the equation of z^4. In this case, r was 2(sqrt2), which raised to the 4th power was 64. The angle value was pi/4, which multiplied by 4 was pi. That's how we get the answer:

64 (cos(pi)+isin(pi)). How this helps!

Answer 2

Following are the calculation to the given value:

Given:

[tex]\to Z= 2+2i[/tex]

To find:

[tex]Z^4=?[/tex]

Solution:

[tex]\to Z= 2+2i[/tex]

[tex]\therefore\\\\i^2= -1[/tex]

[tex](a+b)^2= a^2+b^2+2ab[/tex]

Square the given value:

[tex]\to Z^2= (2+2i)^2[/tex]

         [tex]= 2^2+(2i)^2+2 \times 2 \times 2i\\\\= 4+4i^2+8i\\\\= 4-4+8i\\\\=8i[/tex]

When [tex]Z^2= 8i[/tex] then again square the value

[tex]\to ( Z^2)^2= (8i)^2\\\\\to Z^4= 64i^2\\\\\to Z^4= -64\\\\[/tex]

Therefore, the final answer is "-64".

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Related Questions

Lulu tells her little brother, Jack, that she is holding 20 coins, all of which are either dimes or quarters. They have a value of $4.10. She says she will give him the coins if he can tell her how many of each she is holding. Solve this problem for Jack." How many dimes and quarters in Lulu holding? Enter your final answer in the space below. Please make sure you write your interpretation in a complete sentence

Answers

Given :

Lulu tells her little brother, Jack, that she is holding 20 coins, all of which are either dimes or quarters.

They have a value of $4.10. She says she will give him the coins if he can tell her how many of each she is holding.

To Find :

How many dimes and quarters in Lulu holding?

Solution :

4.10 dollar = 410 cents

Let, number of dimes and quarter are x and y.

So, x + y = 20    ...1)

Also, 10x + 25y = 410    ...2)  

Putting value of 1) in equation 2), we get :

10x + 25( 20 - x ) = 410

10x + 500 - 25x = 410

15x = 90

x = 6

y = 14

Therefore, number of dimes and quarters are 6 and 14 respectively.

Hence, this is the required solution.

HELP ASAP I WILL GIVE 25 POINTS AND MARK BRAINLIST!!!!!!

Answers

Answer:

1. Addition property

2. Division property

3.  Given

next question

1. Distributive

2. Addition

3. Division

4. Given

Step-by-step explanation:

some one please help, lots of points granted !!!!!​

Answers

1) y=-2x+5
2)y=-1/3x
3)y=-2x+4
4)y=-1/3x+1

Can u guys plz give me ALL the following answers to graph 1.

Answers

Slope ~3
y intercept ~7
y= equation ~y=3x+7

How much is 2% of 3.50

Answers

Answer:

.07

Step-by-step explanation:

3.50 * 2% = .07

or

3.50 * .02 = .07

Which of these is a factor of x3 – 3x2 ?
Question 19 options:

A)

x + 2

B)

x + 3

C)

x – 2

D)

x – 3

Answers

Answer:

The answer is D, x - 3.

Step-by-step explanation:

If we factor x^3-3x^2, the result is x^2(x-3).

Answer:

D

Step-by-step explanation:

Given

x³ - 3x² ← factor out x² from each term

= x²(x - 3) ← in factored form

with one of the factors being x - 3 → D

What is the answer will cashapp you

Answers

Answer:

3z + y = 1

Step-by-step explanation:

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

Write an inequality for the graph below.

Answers

Answer:

There are 2 lines, so this is a system of inequalities.

Find the equation of both lines:

The longer line using points (0,6) and (3,3)

Equation is y = -X+6, the inequality becomes y ≥-x+6

The equation for the shorter line:

Using points (5,1) and (6,2)

Equation is y=x-4, the inequality becomes y≤x-4

The system of inequalities is:

y ≥-x+6

y≤x-4

Step-by-step explanation:

what is the correct answer to 4x1 3/8

Answers

Answer:

3/2

Step-by-step explanation:

That's the answer mark me brainliest Please

Answer:

Step-by-step explanation:

4*1 3/8=

4/1 * 11/8=

11/2 or 5 1/2

Is 3xy + 8 = 4y a linear equation ?

Answers

Answer:

No because of the 3xy term. For an equation to be considered linear there has to be one y value for every x value given

The answer is 3xy + 8 = 4y  is not a linear equation.

What are linear equations?

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: 3xy + 8 = 4y

The degree of this equation is 2 and thus the graph of this equation is not linear.

Hence, 3xy + 8 = 4y  is not a linear equation

Learn more about linear equations here:

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Wykonaj mnożenie i zredukuj wyrazy podobne (x+5)(x+4)(x+3).

Answers

Answer:

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

find the perimeter of the shaded figure.

Answers

Answer:

38

Step-by-step explanation:

Count the unit squares for each side, starting from the left it's 7, 10, 7, 2, 2, 6, 2, and 2

Now add them together:

7 + 10 + 7 + 2 + 2 + 6 + 2 + 2 = 17 + 9 + 8 + 4 = 26 + 12 = 38

Answer: 38 units

Step-by-step explanation: Perimeter is asking for the total length of all the sides that make up a figure. The top border is 10 units, the two outer sides are 7 each (14 in total), if you add all the downward facing edges you get another 10 units, and the two inside sides are 2 units each (4 in total).

10+14+10+4 = 38

Pls help! It has to be due by 5pm.

Answers

Answer:

11 and 3/4 in further.

Answer:

I think he has to jump 11 3/4 inches further

Step-by-step explanation:

pls mark me as brainliest!

HELP PLZ!! WILL MAKR BRAINLIEST

Answers

Answer:

See below

Step-by-step explanation:

The y-intercept is -5.5 as per graph

Taking two random points from the graph to find the slope:

(-1, -6) and (1, -5)

Use slope formula: m = (y2 - y1)/(x2 - x1)

m = (-5 - (-6))/(1 - (-1)) = 0.5

The line in slope-intercept form is (y = mx + b)

y = 0.5x - 5.5

or

y = 1/2x - 11/2

Answer:

i don’t think I understand.

Step-by-step explanation:

Add a computer manufacturing company, they produce two different types of computers. They can make 70 laptops per day while making 55 desktop per day. The company has a total of 14 machines to make computers. They can make a total of 905 computers per day. How many machines make laptops and how many make desktops? (QUESTION NUMBER 4 and in the picture is question number 5. PLEASE HELP WITH BOTH

Answers

Answer:

For the second question, 4 busses and 3 cars.

Step-by-step explanation:

It's really simple actually, but sorry I can't come up with an equation. You can just add or multiply students per bus and students per car until you get to 195.  Each bus can hold 45 students, so 45 x 4 = 180. Each car can hold 5 students, so 5 x 3 = 15. In total, 15 + 180 = 195 students.

PLS HELP! ILL MARK BRAINIEST! what is the x and y intercept for this equation?

Answers

x int: (-2, 0) y int: (0,4)

Whats the slope of (6,0) and (2,-2)

Answers

A. /3/2



Is the answer.

One of the zookeepers solved to find Bernard's speed
when he is, healthy using the equation:
x - 41.5 = 13.5.
The other Zookeeper said that to solve for Bernard's
speed when he is healthy, they must use the equation:
41.5 + 13.5 = x.
Which zookeeper is correct? Explain.

Answers

The second zookeeper is correct you need two answers together to get x

Answer:

Well both zookeepers are correct but the second zookeepers answer was more accurate.

Step-by-step explanation:

The first zookeeper gave the equation :

[tex]x - 41.5 = 13.5[/tex]

So , In order to find Benards speed which is denoted as x , we would still have to collect like terms to isolate x.

The second zookeeper gave the equation :

[tex]41.5 + 13.5 = x[/tex]

In this equation the zookeeper had already isolated x so, only simple addition was needed to find Bernard's speed.

This equation is easier to solve.

please help ill give brainliest!

Answers

Answer:

3,14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

The bake sale sold pies for $5.99 each and cakes for $9.99 each. The total number of pies and cakes sold was 25 for $189.75.

Answers

Answer:

profit 40 dollars

Step-by-step explanation:

I want to know what is the formula for an endpoint with the midpoint of a line segement.

Answers

Answer:

Did u actually need the answer or is this another c.hat?

Step-by-step explanation:

what is the y- intercept of the linear function?
y = - 5/2x -1

Answers

Answer:

y = -1

Step-by-step explanation:

Answer:

the y intercept as a point is (0,-1)

otherwise its only -1

Step-by-step explanation:

the form y=mx+b shows that m is the slope which -5/2 in this problem and b is the y intercept which is -1.

mark me brainliest by going to the bottom of this answer and click the button next to comments

Thank you!!!!!!!!

You work in a restaurant, and a family comes in for dinner. You and your co-worker wait on the
table and prepare their food. The family gives you a $11 tip. You want to split the tip evenly with
your co-worker. How much should you give your co-worker?

Answers

Answer:

:$5.50

Step-by-step explanation:

You will give your co-worker $5.5.

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that you work in a restaurant, and a family comes in for dinner. You and your co-worker wait on the table and prepare their food. The family gives you a $11 tip.

For evenly splitting the tip, you will give your co - worker :

{x} = 11/2 = 5.5

{x} = $5.5

Therefore, you will give your co-worker $5.5.

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Write 6.25 in expanded notation.

Answers

Answer:

6.00+0.20+0.05

Step-by-step explanation:

Answer:

6.25 in expanded notation should be written as: (6 x 1) + (2/10) + (5/100).

Step-by-step explanation:

Hope I can really help:).

3y-24 useing the greatest common factor.

Answers

Answer:

In 3y-24, 3 is the greatest common factor.

3y-24

=3(y-8)

Answer:

In 3y-24, 3 is the greatest common factor.

3y-24

=3(y-8)

Step-by-step explanation:

Hope this helped have an amazing day!

The graph below shows a system of equations:
5
y = -x + 5
.
4
3
2
K
+
+0
-1
2
6
y = x - 1
-2
-3
+
-57
The x-coordinate of the solution to the system of equations is
(5 points)

Answers

Answer:

x=2

Step-by-step explanation:

  y=-x+5

-1(y)=(x+1)-1   = -y=-x-1

   y=-x+5

+ -y=-x-1

  0=-2x-4

0=-2x-4

+4     +4

4=2x

1/2(4)=(2x)1/2

2=x

The x-coordinate of the solution to the system of equations is 3.

What is a system of equations?

A system of equations is a set or collection of two or more equations with the same variables. The common solutions are the intersecting points of the equations. The number of equations and unknowns affects the existence and uniqueness of the solution. A system of equations can be classified similarly to single equations.

Given that, the graph given shows a system of equations,

We know that, the solution of the system of equations, is given by the point where the lines intersect,

So, here the lines intersect, at (3, 2)

Therefore, the x-coordinate is 3

Hence, the x-coordinate of the solution to the system of equations is 3.

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PLZ HELP ITS URGENT!!! Which of the following represents the value of the series below? Also maybe if possible, could you please add an explanation?

Answers

Answer:

first one

Step-by-step explanation:

the sum of (9k-4) =3542

so it will be the first one because

28((5+248)/2)=3542

Answer:

a

Step-by-step explanation:

cuz i milk da cows homie, all fo my edge brothas, no cap on jaw, j keepin it real fo yall homies

Solve each equation mentally for x.

x • 7/3 = 1

Your answer must be in the form of a fraction.

Answers

Use Cymath to find your answer.

a conical vessels with base radius 5 cm and height 24cm is full of water this water is emptied into a cylindrical vessel of base radius 10cm find the height to which the water will rise in the cylindrical vessel​
please help me

Answers

Answer:

[tex]2\ cm[/tex]

Step-by-step explanation:

[tex]We\ are\ given\ that,\\Radius\ of\ the\ conical\ vessel=5\ cm\\Height\ of\ the\ conical\ vessel=24\ cm\\Hence,\\As\ we\ know\ that,\\Volume\ of\ a\ cone=\frac{1}{3}\pi r^2h\\Hence,\\The\ volume\ of\ the\ conical\ vessel=\frac{1}{3}\pi (5)^224= \frac{1}{3}\pi 25*24=200\pi \\Hence,\\The\ volume\ of\ the\ conical\ vessel=The\ amount\ of\ water\ filled\ in\ it\\Hence,\\The\ amount\ of\ water\ filled\ in\ the\ conical\ vessel=200\pi\\Lets\ consider\ the\ cylindrical\ vessel:\\Volume\ of\ a\ cylinder=\pi r^2h[/tex]

[tex]As\ we\ are\ not\ said\ that\ the\ cylindrical\ vessel\ was\ empty,\ let\ its\ initial\\ height\ be\ h_1\\Radius\ of\ the\ Cylindrical\ vessel=10\ cm\\Initial\ height\ of\ the\ cylindrical\ vessel=h_1\\Initial\ volume\ of\ the\ cylindrical\ vessel=\pi *10^2*h_1=100h_1\pi \\Initial\ amount\ of\ water\ in\ the\ cylindrical\ vessel=100h_1\pi \\Hence,\\Final\ amount\ of\ water\ in\ the\ cylindrical\ vessel=Final\ amount\ of\ water\\ in\ the\ cylindrical\ vessel +Amount\ of\ water\ in\ conical\ vessel[/tex]

[tex]Hence,\\Final\ amount\ of\ water\ in\ the\ cylindrical\ vessel=100h_1\pi +200\pi \\Now,\\Let\ the\ final\ height\ be\ h_2\\Hence,\\Final\ amount\ of\ water\ in\ the\ cylindrical\ vessel=\pi *10^2*h_2=100h_2\pi \\Hence,\\100h_2\pi =100h_1\pi +200\pi \\Hence,\\100h_2=100h_1+200\\100h_2-100h_1=200\\100(h_2-h_1)=200\\h_2-h_1=2\\Hence,\\As\ the\ rise\ in\ level\ is\ the\ difference\ between\ the\ initial\ and\ final\\ heights:\\The\ rise\ in\ level\ of\ water=2\ cm[/tex]

which expression is equivalent to 2(a+3) when a equals 3

2(3)
5(3)
2(3)+3
2(3)+6​

Answers

2(3+3) or 2(3)+6, so the answer is the third option. It’s just using the distributive property.

Answer:

2(3)+6

Step-by-step explanation:

a = 3

substitute a with 3

2(a+3)

= 2(3+3)

= 2(6)

= 12

i) 2(3) = 6 ❌

ii) 5(3) = 15 ❌

iii) 2(3)+3 = 6+3 = 9❌

iv) 2(3)+6 = 6+6 = 12

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