Mathematics High School

2i^20 + i^42
i^101 - i^2

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Answers

Answer 1

I assume you're talking about a fraction,

(2i ²⁰ + i ⁴²) / (i ¹⁰¹ - i ²)

Remember that i ² = -1; from this it follows that

i ³ = i ² × i = -i

i ⁴ = i ³ × i = (-i ) × i = -i ² = -(-1) = 1

i ⁵ = i ⁴ × i = i

i ⁶ = i ⁵ × i = i ² = -1

and so on. In particular, raising i to some integer multiple of 4 reduces to 1.

Using the above pattern, we find

i ²⁰ = 1

i ⁴² = i ⁴⁰ × i ² = 1 × (-1) = -1

i ¹⁰¹ = i ¹⁰⁰ × i = 1 × i = i

So, we have

(2i ²⁰ + i ⁴²) / (i ¹⁰¹ - i ²) = (2 - 1) / (i - (-1)) = 1 / (i + 1)

We can stop here, but usually it's more useful to have complex numbers written in standard a + bi form. To get this result, multiply the numerator and denominator by the complex conjugate of i + 1:

(2i ²⁰ + i ⁴²) / (i ¹⁰¹ - i ²) = 1 / (i + 1) × (-i + 1) / (-i + 1)

… = (-i + 1) / (-i ² + 1²)

… = (-i + 1) / (-(-1) + 1)

… = (1 - i ) / 2

or equivalently,

… = 1/2 - 1/2 i

Related Questions

30 [tex]30\geq 5[/tex]

Answers

30 is more than 5 not exactlt know what ur looking for here?

Find the solution(s) to the system of equations. Select all that apply.
y=x²-4
y=-x-2

Answers

A and C as they both cross over eachother which determines the answer

The solution will be the intersection points thus options A (1,-3) and B (-2,0) will be correct.

What is a graph?

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

The solution will be the intersection points of both functions.

At the intersection point,

x² - 4 = -x - 2

x² + x - 2 = 0

x² + 2x - x - 2 = 0

x(x + 2) - (x + 2) = 0

(x - 1)(x + 2) = 0

x = 1,-2

At x = 1

y = -1 - 2 = -3 so first intersection is (1,-3)

At x = -2

y = -(-2) - 2 = 0 so second intersection is (-2,0)

Hence "The solution of the given system of equations is (1,-3) and (-2,0)".

To learn more about graphs,

brainly.com/question/24861666

#SPJ2

John eats 0.3 ounces of cake for breakfast each day for 30 days. How many ounces of cake will he eat for 15 day.

Answers

Answer:

He will eat 4.5 ounces of cake over a 15 day span.

Step-by-step explanation:

It's just multiplication. 0.3 x 15

Classify the triangle with angles with measures 33°, 90°, and 57° as acute, right, or obtuse.
A. acute
B. right
C. obtuse

Answers

it’s a right triangle, so B

Answer:

The answer would be B. Right

Step-by-step explanation:

This is because if one of the angles measures 90 degrees, would be a right triangle I believe. (hope this helps)

what's 5x-4y=-12 need help​

Answers

Use Socratic best app
hope this helps !!!!!!

how do you finish graphing your line?

Answers

Answer:

Step-by-step explanation:

Step 1: Identify the variables

Step 2: Determine the variable range

Step 3: Determine the scale of the graph

Step 4: Number and label each axis and title the graph

Step 5: Determine the data points and plot on the graph

Step 6: Draw the graph

JKLM is a rectangle. if JL = 4x - 12 and MK = x, what is the value of x? what is the length of each diagonal?

Answers

Answer:

x = 4

The diagonals are both 4

Step-by-step explanation:

The fact that the two sides have no letter in common indicates that they are opposite each other or a diagonal. In this case the length is a diagonal. Diagonals in a rectangle are equal.

4x - 12 = x                      Add 12 to both sides

4x - 12 + 12 = x + 12      Subtract x from each side

4x - x = 12

3x = 12                           Divide by 3

3x/3 = 12/3

x = 4

One of the diagonals = 4 because it is x.

keith buys 6 pencils for 90p
how much does one pencil cost?
how much would five pencils cost
how much would eleven cost ?

Answers

15p per pencil for 6 pencils
75p for 5 pencils
1.65 for 11 pencils

Answer:

1 Pencil = 15p

5 Pencils = 75p

11 Pencils = 165p --> £1.65

Step-by-step explanation:

To find one pencil... 90 / 6 = 15

To find 5 pencils... 15 (worth 1 pencil) * 5 = 75

To find 11 pencils... 15 (worth 1 pencil) * 11 = 165 which is £1.65

The helicopter can travel 75 miles per hour. How many miles per minute can the helicopter travel?

Answers

Answer:

4.69 miles per minute

Step-by-step explanation:

75 ÷ 60 (60 minutes in an hour) = 4.6875

4.6875 rounded to the nearest hundredth is 4.69

Can you please help me solve this

Answers

On the table, x is in the left column, y is in the right.
Using the equation y = kx, we need to find k for that data
150 = k(1250)
150/1250 = k
0.12 = k

You can confirm that by doing the same with the second row, but I won’t put that here. It’s the same.

Dollars/kilowatt-hour is the label for the k of each equation (0.12, 0.15). We calculated dollars divided by (per) kWh.

Company P is less expensive than company M, because 0.12 < 0.15.

We need to buy 2,375 kWh of electricity from company P. The equation y = kx applies, where y is unknown, k = 0.12, and x = 2,375

y = (0.12)(2375)
y = $285

Let me know if you have any questions.

Mr. DiBello ordered pizzas for a party and organized the information into a table. If Mr. DiBello paid a total of $121.55, how many large pizzas did he order?

Answers

How much does one large pizza cost information is missing

how many solutions does 10t - 6= 10t + 6 have

Answers

i think 7 bc it’s kinda simple? i think..

SOS PLEASE HELP
Write the equation for this line ​

Answers

Y=3x-3
3x is your slope

PLSS HELP ME ASAP!!! I WILL GIVE YOU BRAINLYEST!!! PLSS JUST HELP ME :(

The pyramid below has a rectangular base with an area of 150 square feet. The height of the
Pyramid is 30 feet.
30 ft.

What is the volume of this pyramid in cubic feet?

A. 180
B. 1500
C. 4500
D. 45,000

Answers

Answer:

4500

Step-by-step explanation:

150*30=4500

is Rolling a 4 with one number cube and a 6 with another independent or dependent

Answers

Answer:

it would be independent

Step-by-step explanation:

because the number and the coube are different so they're independent variables

VX
Find the mean of the data set shown below. Round to the nearest tenth, if necessary.
This Week's High Temperatures (°F)
29, 38, 45, 31, 50, 58, 62

Answers

Answer:

44.7

Step-by-step explanation:

Find the mean of the data set shown below. Round to the nearest tenth, if necessary.

This Week's High Temperatures (°F)

29, 38, 45, 31, 50, 58, 62

The formula for the Mean of a given set of data is

= Sum of terms/ Number of terms

Number of terms = 7

Hence,

Mean = 29+ 38+ 45+ 31+ 50+ 58+ 62/7

Mean = 44.714285714286

Approximately to the nearest tenth= 44.7

A large rectangular office measures 9 yards by 15 yards. What is the area of the office?

Answers

Answer:

135

Step-by-step explanation: 9x15=135

135

9x15=135

Hope it helps!!

NOBODY RESPONDED ON MY LAST QUESTIONS BUT I NEED HELP!!!!

Answers

Answer:

Step-by-step explanation:

4a:(3)

4b: d=don dx3=

Solve for Х.
16
20
A 25.6
В
6
С
12
D 15

Answers

Answer:

12 which is on C

Step-by-step explanation:

use pathogoras theorem

a^2+b^2=c^2

16^2+b^2=20^2

256+b^2=400

b^2=400-256

b^2=144

b= square root of 144

b= 12

Which function is equivalent to g of x = x squared + 6x + 8?
A.g(x)=(x+2)(x+4)
B. g(x)=(x-2)(x--4)
C. g(x)=(x+2)(x-4)
D.g(x)=(x-2)(x+4)

Answers

I think A, there are no negatives in this equation

Factor the trinomial
3x^2+12x+9

Answers

Answer:

x^2 + 4x + 3

Step-by-step explanation:

divide everything by 3

Help ASAP I’ll mark you as brainlister

Answers

Answer:

I think 9, sorry if this is wrong

Step-by-step explanation:

Find the length of the missing side leave in simplest radical form

Answers

Answer:

choice 4) sq rt 69 ft

Step-by-step explanation:

13^2 - 10^2

169-100 = 69

sq rt 69

Which statement best describes the main theme of the short story?

A. People act in suprising ways in order to fit in with orders

B. People who bully other people are often Insecure themselves

C. People might not realize that their actions or words are hurtful.

D. People who have a fear of public speaking just need more practice

Story: The Fan Club (Common Lit)​

Answers

Answer:

c- people might not realize there words/actions are hurtful

Please help asap! The numbers for the graph have to be whole! (Can’t be .5)

Answers

put the top point on the first point from the top and the other one on the first point from the bottom.

Evaluate the expression. 5/8 + 1/4

Answers

Answer:

7/8

Step-by-step explanation:

Answer: 7/8 or 0.875

Help!! I have no clue how to do this

Answers

A triangle equals 180° so set up the equation as
58+73+12x+1=180
132+12x=180 (I got 132 by adding 58,73,1)
Subtract 132 from both sides
You should get 12x=48
Divide both sides by 12
X=4
The sum of all the angles in a triangle is 180°.

(12x + 1) + 58° + 73° = 180°

12x + 132° = 180°

12x = 180° - 132°

x = 48°/12

x = 4°

Help me please

Find all real zeros of the polynomial p(x)=2x^3+3x^2-8x-12

Answers

Answer is C B usatestprep

will mark brainliest and rate 5/5

Answers

Answer:

20,250 square yards

Step-by-step explanation:

Formula: s^2 + 2st

75^2 + 2(75)(97.5)

5625 + 14,625

20,250

3
Use the less than, greater than, or equal to symbol
What is this answer?

Answers

Answer:

3 and what

hope this does not help

you cannot compare when there’s only one number...
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