1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Amiraneli [1.4K]
3 years ago
10

Simplify this expression: i ^257

Mathematics
1 answer:
Katarina [22]3 years ago
8 0
Okay! 
What is i? 
i = <span>√(-1)

What is i^2? 
i^2 = </span>√(-1) * <span>√(-1) 

Note: Whenever you multiply two square roots with the same numbers you get this: 

</span><span>√(a^2)
</span>
Or in this case: 

√(-1 * -1) = -<span>√(1) = -1
</span>
So, 
i^2 = -1

What does i^3 equal? 
i^3 = √(-1) * √(-1) * √(-1) = 1 * √(-1) = <span>√(-1) which is... -i
</span>
What does i^4 equal? 
i^4 = √(-1) * √(-1) * √(-1) * √(-1) =  √(-1 * -1 * -1 * -1) = 1

After that the cycle does it thing and cycles back. 
So, with this information we can figure out what i^157 equals. 

Knowing long division here helps a lot!
Take 157 and divide it by 4 using long division. If you don't know it, I'll show you how to do it to the best of my abilities. (Refer to the picture. If you have any questions about it then ask. Even if the question is... what does this say?) 

After using long division we see that we get: 
39 with a remainder of 1. 

What that means is: 
(i^4)^39 is what we have. The remainder of 1 means that we have 1 i left. So our answer is i. 

The reason we divided by 4 and not some other term is because i^4 = 1, so it is easy to work with. In this case (i^4)^39 still just equals 1. Which leaves our remainder as our answer. 

So once again the final answer is: 
i

As for i^257. I'll show you the answer, but I won't give the work for this one. I'd recommend you try it out for yourself. 

i^257 = (i^4)^64 * i = i.

I hope that I helped, and if you have any further questions then ask away! 


You might be interested in
A ball is tossed up in the air at an initial rate of 50 ft/sec from 5 ft off the ground.
Fofino [41]

Answer with Step-by-step explanation:

Since we have given that

Initial velocity = 50 ft/sec = v_0

Initial height of ball = 5 feet = h_0

a. What type of function models the height (ℎ, in feet) of the ball after tt seconds?

As we know the function for height h with respect to time 't'.

h(t)=-16t^2+v_0t+h_0\\\\h(t)=-16t^2+50t+5

b. Explain what is happening to the height of the ball as it travels over a period of time (in tt seconds).

What function models the height, ℎ (in feet), of the ball over a period of time (in tt seconds)?

if it travels over a period of time then time becomes continuous interval . so it will use integration over a period of time

Our function becomes,

h(t)=\int\limits^t_0 {-16t^2+50t+5} \, dt

3 0
3 years ago
Rafiq compares the
Furkat [3]

Answer:

Hey there!

Rafiq's error was that the other number is also changing. He had 4 x 8 and if he had 8 x 8, that would be twice as much, but he used 8 x 12 instead, and  12 is not 8.

Let me know if this helps :)

5 0
3 years ago
A candy jar contains flavored jelly beans. There are 7 orange, 9 cherry, 3 lemon, 15 licorice, and 6 blueberry. Find the probabi
Alisiya [41]

Answer: 0.046

Step-by-step explanation:

From the question,

orange jelly beans= 7

Cherry jelly beans =9

Lemon jelly beans = 3

Licorice jelly beans = 15

Blueberry jelly beans = 6

Total jelly beans = 40

The probability of choosing the first cherry jelly beans will be = 9/40

After the first one is chosen, there'll be 8 cherry jelly beans and total of 39 left. The probability of choosing the second one will be = 8/39

The probability of choosing two cherry jelly beans in a row will be:

= 9/40 × 8/39

= 72/1560

= 0.046

4 0
3 years ago
14. Find the real-number solutions to the equation p3 - 4p2 = 0
forsale [732]

Answer:

p=0 or p=4

Step-by-step explanation:

first simplify the equation

p^3-4p^2=0

p(p^2-4p)=0

p(p-4)(p-0)=0( factorise p^2-4p)

p=0 p=0. p-4=0,p=4

therefore,p=0 or p=4

7 0
3 years ago
there are 100 officials at the race. you read that the total cost of all the officials for one day is 20 654. how much does each
DaniilM [7]

Answer:

$206.54

Step-by-step explanation:


Divide the number of officials by the total days pay to get the pay for each official working the race

3 0
3 years ago
Other questions:
  • Karen read 20 pages of her book in a half hour. If she reads for 3 hours at the same rate , about how many pages of her book can
    14·2 answers
  • The Hundred Years War led to the end of the Middle Ages in the beginning of the
    10·1 answer
  • If you borrow $800 for 8 years at an annual interest rate of 11%, how much will you pay altogether?
    10·1 answer
  • What is the maximum value of P = 4x + 2y, given the constraints on x and y listed below?
    12·2 answers
  • Given the equation f(x)= -10x-4 and g(x)=6-2x, find f(x) - g(x)​
    6·2 answers
  • What does the variable represent in the equation 6-8p=38
    9·2 answers
  • 406 students went on a field trip. Eight buses were filled with 6 students in travel cars. How many were in each bus?
    15·2 answers
  • Because the graph below is misleading, which magazine appears to have about four times the circulation of Circuitry Today?
    5·1 answer
  • Find the surface area of this triangular prism.
    11·1 answer
  • What is the volume of the following cone? What is the capacity?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!