Let z=1+i where i^2=-1.calculate z^2 z^3 z^4

Answers

Answer 1

Answer:

[tex]0[/tex]

Step-by-step explanation:

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

[tex]i=-1[/tex]

Subsite i in for z

[tex]z=1+-1[/tex]

Add [tex]-1[/tex] to both sides

[tex]z=0[/tex]

Anything multiplied by 0 is just 0.


Related Questions

Find the slope of a line that passes through the
following ordered pairs. Reduce to lowest
terms.
(-6, 9) & (2,9).

Answers

Given that,

Point 1 = (-6,9)

Point 2 = (2,9)

To find,

The slope of a line that passes through the given pair.

Solution,

We have,

x₁ = -6, x₂ = 2, y₁ = 9, y₂ = 9.

The formula for the slope of a line is given by :

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\\\=\dfrac{9-9}{2-(-6)}\\\\=0[/tex]

Hence, the slope of the line that passes through the given pair is 0.

A recipe for apricot stuffing calls for 1/2 pounds of apricots. If Gracie
increases the recipe 2 - times, how
2 many pounds of apricots will she
need?

Answers

Answer:

1 pound.

Step-by-step explanation:

1/2 * 2

= 1

Whats 100 divided by 25

Answers

The answer is 4! Think of it like quarters 4 quarters (25 cents) makes a dollar (1.00)

4 is the quotient of 100 divided by 25.

Here, we have,

given that,

100 divided by 25

now, we have to find the quotient of 100 divided by 25.

so, we get,

100 ÷  25

now, using the rule of division,

so, we get,

100/25

=> 20/5

=> 4/1

=> 4

Hence, 4 is the quotient of 100 divided by 25.

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2(x -1) + 1/2 (4x + 6)=5

Answers

X: -4. Y: -3

Step-by-step explanation:

Help please stuck on this !!!!!

Answers

Answer:

rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

Step-by-step explanation:

rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

Find the value of x?

Answers

Answer:

15.09

Step-by-step explanation:

By angle bisector property of a triangle, we have:

[tex] \frac{x}{17.1} = \frac{6}{6.8} \\ \\ x = \frac{17.1 \times 6}{6.8} \\ \\ x = \frac{102.6}{6.8} \\ \\ x = 15.0882353 \\ \\ x \approx15.09[/tex]

You have to spend money to make money. You purchase three social media advertisements for every one newspaper ad you end up purchasing a total of 24 advertisements

Answers

Answer:

x = 3y

x + y = 24

The number of social media advertisement purchased is 18

And, the number of newspaper advertisements purchased is 6

Step-by-step explanation:

Let us assume the number of social media advertisement purchased be x

And, the number of newspaper advertisements purchased be y

As three social media advertisements for every one newspaper advertisement is purchased

So,

y = x ÷ 3

x = 3y

And it is ended by total of 24 advertisement

That means

x + y = 24 ............(1)

Now put the value of x in equation 1

3y + y = 24

4y = 24

y = 24 ÷ 4

= 6

x = 3y

= 6 × 3

= 18

Now  The equations are

x = 3y

x + y = 24

3/5 divided by 2 1/2

Answers

Step-by-step explanation: To divide mixed numbers, first rewrite the mixed numbers as improper fractions.

So here, 3/5 is already a fraction and 2 and 1/2 can be written as 5/2.

Remember that dividing by a fractions means the same thing

as multiplying by the reciprocal of that fraction.

In other words, 3/5 ÷ 5/2 can be rewritten as 3/5 · 2/5.

Finally, multiplying across the numerators and the

denominators, we have 6/25.

The result of the division of 3/5 divided by 2 1/2 is: 6/25.

Here, we have,

given that,

3/5 divided by 2 1/2

To divide mixed numbers, first rewrite the mixed numbers as improper fractions.

So here, 3/5 is already a fraction and 2 and 1/2 can be written as 5/2.

Remember that dividing by a fractions means the same thing

as multiplying by the reciprocal of that fraction.

In other words, 3/5 ÷ 5/2 can be rewritten as 3/5 · 2/5.

Finally, multiplying across the numerators and the

denominators,

we have 6/25.

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Which of the following sets include all rational numbers?

Answers

It's the Second one and the third one

Step-by-step explanation:

Pie is irrational so you can easily cross it off and it leads to to the second one and the third one

Please help me and explain

Answers

Answer:

the answers would be 12/35

because you all the animals together including the wolf and bobcat which is 35. so then you add the wolf and bobcat separately which is 12

Answer:

answer will be 12/35

Step-by-step explanation:

total no. of animal= 16+7+5+7=35andtotal bobcat and wolf =5+7=12so. probability=12/35--------------------------plzzzz mark it as a brilliant ans

A. 1
B. .5
C. .55
D. .10
E. 1.10

Answers

Answer:

E

Step-by-step explanation:

The onlt one that makes sense

E is the correct answer . Hope u got it correct

Find the coordinate of the midpoint of line 5,6 and 5,3

Answers

Answer:

[tex](5,\frac{9}{2})[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Step-by-step explanation:

Step 1: Define

Point (5, 6)

Point (5, 3)

Step 2: Find Midpoint

Substitute:                    [tex](\frac{5+5}{2},\frac{6+3}{2})[/tex]Add:                              [tex](\frac{10}{2},\frac{9}{2})[/tex]Divide:                          [tex](5,\frac{9}{2})[/tex]

Answer:

(5, 4.5)

Step-by-step explanation:

You would want to use the midpoint formula to find the midpoint of line 5,6 and 5,3.

Midpoint formula = [tex]\frac{x1 + x 2}{2} , \frac{y1 + y2}{2}[/tex]

x1 = 5

x2 = 5

y1 = 6

y2 = 3

Plug those into the midpoint formula.

[tex]\frac{5+5}{2} , \frac{6+3}{2}[/tex]

5+5=10/2 = 5

6+3=9/2=4.5

you answer will be (5,4.5)

hope this helps.

On each of Maggie’s bird-watching trips, she has seen at least 36 birds. If she has taken 3 of these trips each year over the past 15 years, at least how many birds has Maggie seen?

Answers

Answer:

Maggie has seen at least 1620 birds.

Step-by-step explanation:

Ok since Maggie sees 36 birds each trip that means she sees 108 birds every year since she takes 3 trips each year. 36×3=108

If she has been doing this for 15 years she has seen at least 1620 birds because 108×15=1620

Which expression is equivalent to 4(x + 3) - 2(-x - 5)?

Answers

Answer:

the last one because when using the distributive property,  you get

4x + 12 - 2x - 10

Answer:

4x + 12 + 2x + 10

Step-by-step explanation:

4( x + 3 ) -2( -x -5 )

1. Multiply 4 and x = 4x

2. Multiply 4 and 3 = 12

3. Multiply -2 and -x = 2x

(turns positive as there are 2 negative signs)

4. Multiply -2 and -5 = 10

(turns positive as there are 2 negative signs)

A video store charges a monthly membership fee of $9, but the charge to rent each movie is only $2 per movie. Another store has no membership fee, but it costs $3.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company?​

Answers

Answer:

6

Step-by-step explanation:

3.50×6=21

2×6=12+9=21

Round to the nearest percent.

From 80 pencils to 152 pencils.

Answers

Answer:

90% Increase

Step-by-step explanation:

80+72=152

72/80= .9

3(1−3x)=2(−4x+7)+5
what is x?

Answers

X=-16. Isolate the variable by dividing each side by the factors that don’t contain the variable

Gary earns $15.00 per hour at his job. He received a 6% raise. What is the dollar amount of the raise? What is the new hourly wage?

Answers

Answer:

$15.90

Step-by-step explanation:

6% → 0.06

15* 0.06 = 0.9

15+0.9= $15.90

$15.90 is going to be your answer

20% of all the children in a class are left handed. 4 children are left handed. How many children are there in the class all together?

Answers

There are 20 students all together.

what is a equation with variables on both side the equals 18

Answers

The equation contains variables on both sides equals 18 can be written as (2x - 18) = x.

What is defined as the linear equation in one variable?

A linear equation would be a type of equation with each variable's degree is completely identical to one.

Linear equations in one variable include those in which only one variable is present and there is only one solution to the equation. When drawn on the a graph, it appears to be either a horizontal or vertical straight line.Unknown quantities can be represented by any variable or symbol, but in most cases, a variable 'x' is used to symbolize the unknown quantity in a linear equation with one variable.

Now, for the given question, the equation which could be represented in the form of variable on both side and has the solution equals to zero is;

(2x - 18) = x

The solution can be obtained as;

2x - 18 = x

Bring variable part on one side and constant on other.

2x - x = 18

x = 18.

Therefore, the equation with variables on both side the equals 18 is obtained as  (2x - 18) = x.

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A builder buys 26.5 acres of land to develop a new community of homes and parks. Part 1 out of 2 The builder plans to use 0.25 of the land for a park. How many acres will he use for the park?

Answers

Answer:

6.625 acres

Step-by-step explanation:

What we know:

A builder brought 26.5 acres of land to develop a community.

A fourth of that land will be used to make a park.

1/4 * 53/2

LCM of 4 and 2 is 4

1/4 * 106/4

106/16 = 53/8 = 6.625 or 6 5/8 acres will be used for a park

Answer:

6.625 acres

Step-by-step explanation:

26.5 * 0.25 = 6.625

Which expression is equivalent to −2(5x + 3y)?

3y(5x − 2)
5x(−2 + 3y)
−10x − 6y
−10x + 3y

Answers

Answer:

−10x − 6y

Step-by-step explanation:

−2(5x+3y)

=(−2)(5x+3y)

=(−2)(5x)+(−2)(3y)

=−10x−6y

6x+5=35
Solve the equation

Answers

Its x=5 hope this helpsss!!

Answer:

x = 5

Step-by-step explanation:

6x + 5 = 35

     -5     -5

6x = 30

divide both sides by 6

x = 5

Hope this helps!!!!

Find the measure of angle BCD

Answers

Answer: D

Step-by-step explanation:

10. A hobby pack of baseball cards contain 9 cards and a jumbo pack
contains 35 cards. Ethan bought 7 packs for a total of 141 cards. How
many packs of hobby and jumbo did Ethan buy?

Answers

Answer:

He bought 3 jumbo packs and 4 hobby packs.

Step-by-step explanation:

Ethan bought 4 number of hobby packs and 3 number of jumbo packs.

What are Linear Equations?

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Let x be the number of hobby pack that Ethan buy and y be the number of jumbo packs that Ethan buy.

Ethan bought 7 packs for a total of 141 cards.

We got two linear equations here :

x + y = 7

9x + 35y = 141

Multiplying the first equation throughout by 9,

9x + 9y = 63

Subtracting the resulting equation we get from the second equation,

(9x + 35y) - (9x + 9y) = 141 - 63

35y - 9y = 78

26y = 78

y = 3

x = 7 - y = 4

Hence Ethan bought 4 hobby packs and 3 jumbo packs.

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I need help right away
Graph the following piecewise function. x^2+2 if -5

Answers

Answer:

4

Step-by-step explanation:

Hope this helps

A pilot takes a taxi from the airport to a hotel. The taxi driver charges a $2.50 initial charge plus $2.65 per mile. Which equation can be used to find y, the total cost of the trip, if x represents the number of miles of the trip?Y=2.65x+2.50y=2.50x+2.65y=2.65(x+2.50)y=2.65x−2.50

Answers

Answer:

Y=2.65x+2.50

Step-by-step explanation:

Given that:

Initial charge = $2.50

Charge per mile = $2.65

Find the total cost (y) of the trip ; if number of miles = x

Total cost of trip = initial charge + (charge per mile * number of miles)

y = $2.50 + ($2.65 * x)

y = $2.50 + $2.65x

Whats The Answer Marking Brainliest, Please explain your answer:D...

Answers

D.
the absolute value of 15 is greater than the absolute value of -10, 15 dollars is more than 10

idk this please help me ​

Answers

Answer:

Pretty sure it is c

Step-by-step explanation:

3
4
Piper paid for 3 boxes of cookies to be
delivered to her house.
• Each box of cookies cost $24.95.
• Piper paid $12.99 for delivery.
What is the total amount Piper paid?

Answers

Answer:

Total Amount Paid by Piper = $84.87

Option C is correct.

Step-by-step explanation:

Total boxes of cookies = 3

Cost of 1 box of cookie = $24.95

Delivery charges paid = $12.99

We need to find total amount Piper paid.

First we will find cost of 3 boxes of cookies:

Cost of 1 box of cookie = $24.95

Cost of 3 box of cookie = $24.95 x 3

                                        = $74.85

Now, add cost of 3 boxes of cookies with delivery charges paid to get total amount paid.

Total Amount Paid = Cost of 3 box of cookie + Delivery charges paid

                               = 74.85 + 12.99

                               = 87.84

So, Total Amount Paid by Piper = $84.87

Option C is correct.

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