Simplify the following expression using imaginary numbers. Express your answer in a + bi form
i^80+i^38-i17 please show work

Answers

Answer 1
Answer:

0 - 17i

Step-by-step explanation:

Given expression;

i⁸⁰ + i³⁸ - i17

To express the expression in the form a+bi;

i. Rewrite the expression such that it contains terms in i²

(i²)⁴⁰ + (i²)¹⁹ - i17

ii. Solve the result from (i) above using the identity i² = -1

We know that the square root of -1 is i. i.e

[tex]\sqrt{-1} = i[/tex]

Squaring both sides gives

=> [tex](\sqrt{-1} )^{2} = i^{2}[/tex]

=> -1 = i²

Therefore,

i² = -1

Substitute i² = -1 in step (i) above

(-1)⁴⁰ + (-1)¹⁹ - i17

(iii) Solve the result in (ii)

We know that the when a negative number is raised to the power of an even number, the result is a positive number. If it is raised to the power of an odd number, the result is a negative number. Therefore,

(-1)⁴⁰ + (-1)¹⁹ - i17 becomes

1 + (-1) - i17

0 - i17

(iv) Write the result from (iii) in the form a+bi

0 - 17i


Related Questions

what is the area of 9 cm 3 cm of the rectangle​

Answers

Answer:

27cm²

Step-by-step explanation:

it should be the area of rectangle..

Answer:

Step-by-step explanation:

27 sq cm

please help!
Find the area of the circle.
Use 3.14 for pi

Answers

Answer: 153.94

Step-by-step explanation: Formula for area of a circle: pi * r^2

First find the radius by dividing the diameter by 2: 14/2 = 7

Then plug the radius, 7, and pi, 3.14, into the formula:

(3.14) * (7^2) = 153.94 inches squared

Please help me with my work

Answers

321 because you need to use the formula

Answer:

[tex]9600 \: {ft}^{2} \\ [/tex]

Step-by-step explanation:

Area of front rectangle -

= 2 ( length × breadth )

= 2 ( 40 × 30 )

= 2 ( 1200)

[tex] = {2400 \: ft}^{2} \\ [/tex]

Area of other rectangles -

= 4 ( length × breadth )

= 4 ( 60 × 30 )

= 4 ( 1800)

[tex] = 7200 \: {ft}^{2} \\ [/tex]

Surface area of the rectangular prism

[tex] = {2400 \: ft}^{2} + {7200 \: ft}^{2} \\ = {9600 \: ft}^{2} \\ [/tex]

HEY NO LINKS I WILL CALL THE PLACE AND REPORT YOU. BUT IF YOU ANSWERIT AND SHOW STEPS I WILL GIVE YOU BRAINLIEST

Answers

Answer:

Step-by-step explanation:

1. slope = 2, initial value = 5

equation :  y = 2x+5

2. slope: (3-6)/5 = -0.6; initial value = 6

equation : y = -0.6x+6

3. slope : (5- -1)/2 = 3; initial value = -1 -2*3 = -7

equation : y = 3x -7

4. Sorry, cannot see the last point.

Please help solve the question in the image

Answers

Answer:

✅On average Albany gets 20.967 inches rain pee year and Zachary gets 25.153 inches rain per year.

✅On average, it rains more in Zachary in a year.

Step-by-step explanation:

Mean annual rainfall on average = total amount of rainfall for the period of years ÷ 10

✔️Mean Annual rainfall for Albany (in.):

= (22.82 + 19.83 + 28.40 + 23.35 + 30.78 + 21.34 + 11.20 + 17.04 + 18.63 + 16.28) ÷ 10

= 20.967

✔️Mean Annual rainfall for Zachary (in.):

= (26.41 + 23.54 + 30.02 + 26.35 + 34.24 + 25.74 + 18.98 + 21.26 + 23.61 + 21.38) ÷ 10

= 25.153

✅Therefore, on average Albany gets 20.967 inches rain pee year and Zachary gets 25.153 inches rain per year.

✅On average, it rains more in Zachary in a year.

According to the dimensions given on the right rectangular
prism, what is the volume? Fill in the blank with an answer
rounded to the nearest hundredth.

Just type the number. You do not need to type the units.

Answers

Answer:

26.67

Step-by-step explanation:

8 x 5 x 2/3 = 80/3 = 26.67

What is the equation of the line in slope-intercept form?

Answers

Answer:

y = - 1/2x =0

Step-by-step explanation:

y = mx  + b

b = intercept

m = slope

The intercept is 0.

Slope: 0 - 1 / 0+2

Slope = -1/2

A circle is centered at the point (-7, -1) and passes through the point (8, 7).
The radius of the circle is____ units. The point (-15,___ ) lies on this circle..

I will give Brainliest

Answers

Answer:

Step-by-step explanation:

radius =( (8+7)^2 + (7+1)^2 )^1/2 = 17 unit

Equation of the circle = (x + 7)^2 + (y+1)^2 = 17^2

                                   = (-15+7)^2 + (y+1)^2  = 17^2

                                  =14

(-15, 14) lies on this circle

What is the value of Z?

Answers

Answer:

2

Step-by-step explanation:

2(z)+2 = 4

2z = 2 x 2 = 4

Josiah was testing to see the distance his remote would work with his drone. He was
standing in a valley that was 15.75 feet below sea level. His drone lost a connection when it
was 56-feet above sea level. What is the range on his drone remote? (Draw a picture to help)

Answers

Answer: please tell me if you got the answer to this problem. I’ve been looking for the past 2days. :)

Step-by-step explanation:

whatss the diffrence

Answers

There is no difference they are the same

Help please I need this answered so I can go to a party tomarrow. help!

Answers

Answer:

D.

Step-by-step explanation:

8 * 4 = 32 and 14*4=56 cm therefore the perimeter is scaled 4x larger.

tomorrow* not tomarrow.

How many positive whole numbers less than or equal to 360 are divisible by 2 or 3, but are not divisible by 18?

Answers

Answer:

You can do this through trial and error.

The answer is 260.

Step-by-step explanation:

Off the bat, we know all even numbers are multiples of 2 so 180 numbers to be precise. Now we find how many even Numbers are divisible by 18 so all factors of 18 should be satisfactory so 18, 36 etc. there are 20 of those so 180 - 20 = 160

now multiples of 3.  360 dived by 3 is 120 - 20 =100, 100+160 = 260

plz help 20 points pllllllllllllllllllllllz help mee asap

Answers

Answer:

b=4  c=7

Step-by-step explanation:

I think not positive

Answer:

453+557 = 1010

hence b is 5 and c is 3

1. Find the value of x.

A. 94
B. 76
C. 88
D. 82

Answers

Answer:

76

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)

94 = 1/2(x+112)

Multiply each side by 2

2*94 = x+112

188 = x+112

Subtract 112

188-112 =x

76 =x

Could anyone offer a step by step on how to solve this problem?

Answers

Answer:

[tex]m\angle 1 = 40^\circ[/tex]

Step-by-step explanation:

First, notice that the two lines are parallel as indicated by the arrow.

Therefore, by the Alternate Interior Angles Theorem:

[tex]\angle 1\cong \angle 2[/tex]

So:

[tex]m\angle 1 = m\angle 2[/tex]

Substitute:

[tex](2x+20)=(3x+10)[/tex]

Solve for x. Subtract 2x from both sides:

[tex]20=x+10[/tex]

And subtract 10 from both sides:

[tex]x=10[/tex]

We know that:

[tex]m\angle 1 = 2x+20[/tex]

Substitute. Hence:

[tex]m\angle 1 =2(10)+20=40^\circ[/tex]

A coffee shop offers coffee either iced or hot in sizes small, medium, and large. The flavor options are vanilla,
hazelnut, and caramel. If you received a coffee at random, what is the probability you would receive a large,
iced, hazelnut coffee?

Answers

Answer:

1/18

Step-by-step explanation:

There are 2 x 3 x 3 = 18 combinations of coffee.  Only one is large, iced and

hazelnut

So, the probability is 1/18

Need help ASAP much appreciated

Answers

Answer:

If the terms on the left hand side of the equals are the same as the terms on the right hand side of the equals, there will be infinite solutions

Step-by-step explanation:

If the terms on the left hand side of the equals are the same as the terms on the right hand side of the equals, there will be infinite solutions

12x+24x +18 = 36x +24 -6

Combining like terms

36x+18 = 36x +18

Subtracting 36x from each side

18 = 18

This is always true so  it does not matter what x is, the left had side will equal the right hand side

Eleisha is standing facing East. She turns in a clockwise direction and is now facing West. Through how many degrees did Eleisha turn.

Answers

Answer:

180 degrees

Step-by-step explanation:

East and west are two opposite directrions along the same line.

The angle is 180 degrees.

Answer: 180°

Step-by-step explanation: The directions on a compass would look something like this; (Refer to the image.)

A full circle is 360°. Half of 360 is 180. You would have to make a clockwise rotation by 180° to face West. Think of this picture as a clock or a circle.

I hope this helps!

                                     

D. (-7,1) PLEASE HELPPPPPPP ASAAAPPPPP

Answers

Answer:

2,3 and -1,7

Step-by-step explanation:

Tenemos 2 garrafas una al 20% y otra al 30%. Cual es su capacidad de las garrafas si tenemos 12 litros de agua

Answers

Answer:

Cada garrafa tiene una capacidad de 24 litros.

Step-by-step explanation:

Tenemos dos garrafas, definamos V como el volumen que cada garrafa tiene.

Sabemos que una de las garrafas tiene el 20%, entonces el volumen de agua que tiene esta garrafa es:

(20%/100%)*V

Y la otra garrafa tiene el 30%, entonces esta garrafa tiene:

(30%/100%)*V

El volumen total de agua es la suma de esos dos volúmenes, que nos da:

(20%/100%)*V + (30%/100%)*V

Y sabemos que tenemos 12 L de agua, entonces podemos escribir la ecuación:

12 L = (20%/100%)*V + (30%/100%)*V

Ahora podemos resolver esto para V.

12L = 0.2*V + 0.3*V

12L = 0.5*V

12L/0.5 = V

24L = V

Cada garrafa tiene una capacidad de 24 litros.

Which form do you prefer when finding the vertex of a quadratic function, vertex or standard? Why?

Answers

While the standard quadratic form is a x 2 + b x + c = y , the vertex form of a quadratic equation is y = a ( x − h ) 2 + k .

HURRRYYYY PLZZZZ ANSWERRR FASTTTTT

The graph represents a mechanic’s labor costs for a given number of hours of car repair.

Which statement describes the relationship between labor cost and time for a car repair?

All repairs requiring 1 hour or less have the same labor cost.
Labor costs the same no matter how many hours are used for a repair.
Labor costs for a repair are more expensive as the number of hours increases.
There is no cost of labor for a repair requiring less than 1 hour.

Answers

Answer:

A on E2020--All repairs requiring 1 hour or less have the same labor cost.

Step-by-step explanation:

I hope this is correct, if not let me know and I will fix it. I'm sorry in advance if this is incorrect.


Can I get some help with this?

Answers

The answer would be A because the +5 tells you that the vertex of the parabola is y=5

A chair rental company charges $100 for delivery plus $3 per chair.
Write an explicit function for the total cost, T(c), of renting c number of
chairs.

Answers

Answer:

T(c) = 100 + 3*c

Step-by-step explanation:

cost = fee + cost per chair * number of chairs

T(c) = 100 + 3*c

Answer:

T ( c)= $ 100 + $ 3 c

Step-by-step explanation:

Given that :-

Fee for delivery = $ 100Cost per chair = $ 3No. of chair = c

To Find :-

Total cost T( c) of renting c no. of chairs.

Solution :-

Total Cost, T ( c) = Fee + cost per chair × no. of chairs.

T ( c) = $ 100 + $ 3 × c

T ( c) = $ 100 + $ 3 c

HELP








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Answers

i think the ans is -9/8

Answer:

-9/16  is the answer

Which of the following expressions are equivalent?

1. 5(a + 3)

2. 5a + 15

3. 3(2a + 5)

Answers

Answer:

1 and 2 are equivalent

For 1 , use distributive property. Distribute 5 to a and 3. 5 x a = 5a, and 5 x 3 = 15. Therefore, 5a + 15. This is why 1 is equivalent to number 2.

Uhh How do I do this, please answer, anyone

Answers

Answer:

3rd one down is the answer

Answer:

Well let's count how many 65's there are, there are 3

So there needs to be 3 dots on the data plot on top of the section, 65.

Let's exclude some answers, D and B since they don't have 3 hovering over the 65(since there are three 65's).

Let's count how many 67's there are, there are 4.

We need to get rid of any answers that are more than 4 or less than 4 that are hovering over the section of 67. There are no answers to get rid of, let's move onto the next number, 68! There are four 68's. Let's also get rid of any answers that have more than 4 or less than 4 on the section above 68 since we're looking at that number. C is our answer!

Johanna buys two poster frames that have the same area, but different shapes. One is a rectangular frame with a width of 40 inches and a length of 30 inches. The other frame is square. What a poster with dimensions of 36 inches X 36 inches fit in the square frame?

Answers

Answer:

No, the poster would not fit in the frame

Step-by-step explanation:

A rectangle is a quadrilateral (has 4 sides and 4 angles) with two pair of opposite and equal sides.

A square is a quadrilateral in which all sides are equal.

Given that the rectangular frame has a width of 40 inches and a length of 30 inches. The area of the rectangular frame is:

Area of rectangular frame = length * breadth = 40 inches * 30 inches = 1200 in²

Since the square frame has the same area as the rectangular frame, hence:

Area of square frame = length * length

length² = 1200

length = √1200 = 34.64

Therefore the dimensions of the square frame is 34.64 inches by 34.64 inches.

Hence a poster with dimensions of 36 inches X 36 inches cannot fit in the square frame.

the quotient of n and 6
ASAP I need an answer today will give 100 points and mark brainliest PLSSSSSSSSS :)

Answers

Answer:

The quotient of n and 6 is n/6, as quotient means divide.

for example, if it was "the quotient of 24 and 6", it would be 24/6, which is 4.

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