What is the value of iota to the power 19 + iota to the power 20

Answers

Answer 1

Answer:

1 - i

Step-by-step explanation:

[tex] {i}^{19} + {i}^{20} \\ \\ = {i}^{18} .i + {i}^{20} \\ \\ = {( {i}^{2} )}^{9} .i + {( {i}^{2} )}^{10} \\ \\ = {( - 1)}^{9} .i + {( - 1)}^{10} \ \\ ( \because \: {i}^{2} = - 1) \\ \\ ( - 1).i + 1 \\ \\ = - i + 1 \\ \\ = 1 - i[/tex]


Related Questions

Prove that (Root of Sec A - 1 / Root of Sec A + 1) + (Root of Sec A + 1 / Root of Sec A - 1) = 2 cosec A

Answers

Answer:

The answer is below

Step-by-step explanation:

We need to prove that:

(Root of Sec A - 1 / Root of Sec A + 1) + (Root of Sec A + 1 / Root of Sec A - 1) = 2 cosec A.

Firstly, 1 / cos A = sec A, 1 / sin A = cosec A and tanA = sinA / cosA.

Also, 1 + tan²A = sec²A; sec²A - 1 = tan²A

[tex]\frac{\sqrt{secA-1} }{\sqrt{secA+1} } +\frac{\sqrt{secA+1} }{\sqrt{secA-1} } =\frac{(\sqrt{secA-1)}(\sqrt{secA-1})+(\sqrt{secA+1)}(\sqrt{secA+1}) }{(\sqrt{secA+1})(\sqrt{secA-1}) } \\\\=\frac{secA-1+(secA+1)}{\sqrt{sec^2A-secA+secA-1} } \\\\=\frac{2secA}{\sqrt{sec^2A-1} } \\\\=\frac{2secA}{\sqrt{tan^2A} } \\\\=\frac{2secA}{tanA} \\\\=\frac{2*\frac{1}{cosA} }{\frac{sinA}{cosA} }\\\\= 2*\frac{1}{cosA}*\frac{cosA}{sinA}\\\\=2*\frac{1}{sinAA}\\\\=2cosecA[/tex]

SOMEONE PLEASE HELP ME I WILL GIVE BRAINLY

Answers

C have a wonderful day and good luck with school :)

Answer:

C

Explanation:

A function always goes along the x-axis and never repeats

A, B and D repeat on the x-axis so C is your answer


Graph y = -3/2 x-3

It would be helpful if you wrote the coordinates I have to change them to !!!

Answers

Answer:

(-2,0),(0,-3)

Step-by-step explanation:

Set x to zero to find the Y intercept which is (0,-3)

Set Y to zero and use algebra to find out the x intercept which is (-2,0)

p(x)=(1)/(x+1) and q(x)=(1)/(x-1) perform the operation that results in another rational expression p(x)/q(x)

Answers

9514 1404 393

Answer:

  p(x)/q(x) = (x -1)/(x +1)

Step-by-step explanation:

  [tex]p(x)\div q(x)=\dfrac{1}{x+1}\div\dfrac{1}{x-1}=\dfrac{1}{x+1}\times\dfrac{x-1}{1}\\\\ \boxed{\dfrac{p(x)}{q(x)}=\dfrac{x-1}{x+1}}[/tex]

Una persona toma un préstamo de $ 7500 para su liquidación en 6 amortizaciones mensuales iguales, con una tasa de interés del 2.5% mensual. Calcular la amortización y el valor de la cuota a pagar en el tercer mes.

Answers

Answer: $1,266.697.

Step-by-step explanation:

given data:

loan amount =  $7500

duration = 6 months

interest rate = 2.5%

Solution:

[tex]A = P \frac{i(1+i)^{n} }{(1+i)^{n} -1}[/tex]

i = [tex]\frac{2.5}{100} \\= 0.025\\\frac{0.025}{6} \\= 0.004167[/tex]

=

= [tex]7500(\frac{0.00427}{0.0253} )[/tex]

= [tex]7500(0.169)[/tex]

= $1,266.697

Cho is making a rectangular garden, where the length is x feet and the width is 2x + 8 feet. He wants to add garden stones around the perimeter of the garden once he is done.

If the garden is 5 feet long, how many feet will Cho need to cover with garden stones?

Cho will need to cover _______ feet with garden stones.

Answers

Answer:

38 feet

Step-by-step explanation:

P(x) = ℓ(x) + ℓ(x) + w(x) + w(x)

      = x + x + (4x - 1) + (4x - 1)

      = (x + x + 4x + 4x) + (-1 -1)

      = 10x - 2

P(4) = 10(4) -2 = 38

The perimeter is 38 feet when the length is 4 feet long, so Cho will need to

cover 38 feet with garden stones.

QUESTION SHOWN ON PHOTO.

Answers

All of the points on the graph could represent rational numbers. (-1, 0, 1, 4.5)

Answer:

B

Step-by-step explanation:

A: false, point C isn't a rational number

B: True, Every negative integer is a negative rational number, like point A

C: false, point D is a fraction, therefore, point D is a rational number

D: false, like said in A, point C isn't a rational number

how many solutions does 6x-1=2x+5+4x-6

Answers

Answer:

(−∞,∞)

Step-by-step explanation:

I think this is the answer

Answer:

Infinante solutions

Point Q is the midpoint of AB. Q has coordinates of (-2, 4) and A has coordinates of (4,6). What are the coordinates of point B?

Answers

Step-by-step explanation:

Let (x, y) be the coordinates of point B.

(4, 6) => (-2, 4) => (x, y)

We have 2(-2) = 4 + x and 2(4) = 6 + y.

Solving these, we get x = -8 and y = 2.

Hence the coordinates of point B is (-8, 2).

Point Q is the midpoint of AB. Q has coordinates of (-2, 4) and A has coordinates of (4,6). Hence the coordinates of point B will be (-8, 2).

What are the coordinates of the midpoint of the line segment AB?

Suppose we've two endpoints of a line segment as:

A (p,q), and B (m,n)

Then let the midpoint be M(x,y) on that line segment.

Then, its coordinates are:

[tex]x = \dfrac{p+m}{2}[/tex]

and

[tex]y = \dfrac{q+n}{2}[/tex]

Let (x, y) be the coordinates of point B.

Q has coordinates of (-2, 4).

A has coordinates of (4,6).

A (p,q) = (4, 6)

M(x,y)=  (-2, 4)

B = (x, y)

We have

2(-2) = 4 + x

2(4) = 6 + y.

Solving these, we get

x = -8 and y = 2.

Hence the coordinates of point B will be (-8, 2).

Learn more about midpoint here;

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Determine the domain on which the following graph of f(x) is negative. ​

Answers

Answer:

there is no graph.

Step-by-step explanation:

Write the slope-intercept form of the equation of the line through the given point and slope.

through: (-2,-2) slope:


A.y = 3x - 1

B.y = 2x +3

C.y = x + 7

D.y=x

Answers

Answer:

hmmmm

Step-by-step explanation:

Write each equations in standard form.
10.y + 1 =X+2
13.y 4=-K-1)

Answers

Answer:

10. -x + y = 1.

Step-by-step explanation:

10. y + 1 = x + 2

y - x = 2 - 1

-x + y = 1.

v. If ∆PQR≅∆ XYZ then which statement is true.
a.

b. c.

Answers

If ∆PQR≅∆ XYZ

that means PQ≡XY;QR≡YZ;PR≡XZ

A grill at Rudy's restaurant will be used to cook sausage links that are2 lb each and briskets that are 8 lb each. No more than 140 lb of sausage links and briskets will be cooked on the grill for a graduation party.

Answers

Answer:

Step-by-step explanation:

The first one is correct.

Answer:

The firest one( 2x + 8y ≤ 140 )

Step-by-step explanation:

What is the additive inverse of the number 1.6?
≈A. -1.6
≈B. 0
≈C. 1
≈D. 6.1

Answers

Answer:

The additive inverse is -1.6

Answer:

-1.6

Step-by-step explanation:

only doing this so the this so the other person can get brainlyest

Have a great day

drake gathers half of the money he had saved up plus the $50 his father gave him to buy a new scooter that costs $125. Write an equation to help you determine the amount of money drake has saved up.

Answers

Answer:

let x = amount of money saved up

x/2 + 50 = 125

Step-by-step explanation:

“[The city’s engineers excelled in areas] neglected by the Greeks, such as the construction of roads and aqueducts, and of sewers that could wash the filth of the city into the Tiber. They have built paved roads throughout the country, leveling ridges and filling up hollows, so as to make possible the movements of heavily loaded wagons. . . . And such is the quantity of water brought in by the aqueducts, that veritable rivers flow through the city and its sewers: almost every house has cisterns, waterpipes, and copious fountains.”
—Strabo, as quoted in
Empires Ascendant: Time Frame 400 B.C.–A.D. 200

What area of engineering did the Greeks neglect?
a.
buildings
c.
monuments
b.
roads
d.
arches


Please select the best answer from the choices provided

A
B
C
D

Answers

Answer:

the greeks neglected roads

b. roads

Answer:

B. roads

Step-by-step explanation:

The other person got it correct

Could you guys help me ? I'll give brainliest

Answers

When you raise a number to a negative exponent, change the exponent to a positive and make the complete number a fraction with 1 as the numerator.

5 ^-2 = 1/5^2

The answer is C.

Write an inequality to fit the given inequality the line pass through (0,1) and (1,3)​

Answers

Answer: Y< 2/1x +1

Step-by-step explanation: (Slash mark means a fraction)

What is the area of square FGHI?​

Answers

Answer:

Step-by-step explanation:

To get a length of any side 8+10=18

the area= L^2=

                18^2=324m

HELP NEED FAST!!!!!!

Which graph shows a negative slope and a positive y-intercept?

Answers

Answer:

the second one on the top right

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

You can tell by where the line crosses the y-intercept as a positive, and the direction in which the line is going tells you it has a negative slope

You are going on a trip. To get to the beach, you have to drive 475 miles. If you can average 50 miles per hour on your drive, which equation shows how much farther you have to drive over time?

Answers

Answer:

C= -50x+475

Step-by-step explanation:

Step one:

given data

distance travelled = 475miles

velocity = 50miles per hour

let the distance you cover per hour be x

hence per hour, your distance decreases by 50x hours

Required:

The expression for the distance remaining

Step two:

let the distance remaining be C

hence the expression

C= -50x+475

Answer:

The answer is in the picture.

A company uses 6,000 gallons of
water each month. If they reduce their
monthly water use by 12%, how much
water will be saved each month?

Answers

Answer:

5280

Step-by-step explanation:

2x + 9 > 21
solve the inequality

Answers

Answer:

x>6

Step-by-step explanation:

2x + 9 > 21

2x > 21-9

2x>12  dividing by 2

x>12/2

x>6

hope this helps

Answer:

x > 6

X has to be smaller than 6

Tanya wants to buy a sweater that is on sale for 20% off. If the sweater originally costs $10.52, what is the amount of the discount?

Answers

Answer:

$2.10

Step-by-step explanation:

Well 20% is basically 0.2

So 10.52 X 0.2 = $2.104 discounted

I think you need to round this because money is the unit so

$2.10 is your answer.

Answer:

2.10

Step-by-step explanation:

2 milliliters is how many teaspoons?

Answers

Answer:

0.405768

Step-by-step explanation:

In 4 days, the price of a share of stock rose 3/4 of a point. On average, what was the change in stock price everyday

Answers

Answer:

3

Step-by-step explanation:

If you multiply 3/4 and 4 days together you will get 3 so the answer is 3

Please answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!

Answers

Answer:

?

Step-by-step explanation:

DGF I think is right I’m pretty sure

please help i will give brainlest ​

Answers

Answer:

Option 1 and 3

Step-by-step explanation:

Option 1

Use point (0, 11)

y - 11 = 0 ⇒ y = 11 ⇒ correct

Option 2

Incorrect for any point

Option 3

Use point (2, -1)

y + 1 = 0 ⇒ y = -1 ⇒ correct

Option 4

Use point (3, -7)

y - 7 = 0 ⇒ y = 7 ⇒ incorrect

Insert some division signs to make the correct equality 2 8 7 4 = 1

Answers

Answer:

28 / 7 /4 = 1

Step-by-step explanation:

Division Signs to make the correct equality are 2 8/ 7 / 4 = 1

What is equality?

In mathematics, the equal sign denotes parity between quantities, equations, or expressions written on either side. Equal to is represented by two thin, parallel horizontal lines. The "equal to" sign is used to indicate that two items are the same or equal. For instance, 1 + 1 = 2.

A division sign exists the symbol ÷ used between two numerals to demonstrate that the first number maintains to be divided by the second.

Given,

a = 28/7 = 4

b = 4/4 = 1

To know more about  division sign refer to :

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