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
Evaluate 3x +2y - 4z/x for x =5, y=-2,z=10
Evgen [1.6K]

3x + 2y - 4z/x for x=5, y=-2, z=10

3x + 2y - 4z/x

3(5) + 2(-2) - 4(10)/(5)

15 - 4 - 40/5

15 - 4 - 8

11 - 8

3

3 0
3 years ago
Which statement is true about this data set? {43, 46, 48, 57, 42, 47, 48, 44, 46, 45, 48}
vfiekz [6]

Answer: D) 57

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Find the median, lower quartile, and upper quartile for the set of data.
harkovskaia [24]

\text{Find the median:}\\\\\text{To find the median, you would cross out the numbers from the side}\\\text{until you're left with the remainders. Put them in order and solve}\\\\1, 2, 4 ,5, 6, 7, 8, 9, 10, 11\\\text{Add 6 and 7 then divide by 2}\\\\6+7=13\\\\11\div2=6.5\\\\\boxed{\text{The median is 6.5}\\}\\\\\text{The lower quartile is the median of the numbers less than the median, so}\\\text{the numbers from 1-6}\\\\\text{When you cross out the numbers, you would be left with 4}

\boxed{\text{The lower quartile is 4}}\\\\\text{Do the same for the upper quartile for the numbers greater than half}\\\text{of the data set}\\\\\boxed{\text{Your upper quartile would be 9}}

8 0
3 years ago
Read 2 more answers
A bag contains a number of marbles of which 35 are blue, 10 are red and the rest are
photoshop1234 [79]

Answer:

Y = 45*p(y) / (1 - p(y))    if I knew what p(y) is, we can find how many yellow marbles there are.   p(y) = probability of choosing yellow.

Step-by-step explanation:

Total marbles =  35 + 10 + yellow

If probability of choosing yellow =p(y) = yellow/Total

p(y) =  Y/(35 + 10 + Y)

Solve for Y,

p(y)*(35 + 10 + Y) = Y

45*p(y) + p(y)*Y = Y

45*p(y) = Y - p(y)*Y

Y = 45*p(y) / (1 - p(y))

7 0
3 years ago
A school class went on a field trip to see a magician perform there were 17 females 20 males in the class the magicians randomly
8090 [49]

Answer:

P(A) = 37/100, P(A) = 37%

Step-by-step explanation:

Probability of an event = \frac{Number of favorable outcomes}{Total number of outcomes}

3 0
3 years ago
Read 2 more answers
Other questions:
  • (01.02 MC)The number line shows the distance in meters of two divers, A and B, from a shipwreck located at point X:
    9·1 answer
  • A scientist inoculates mice, one at a time, with a disease germ until he finds 2 that have contracted the disease. if the probab
    6·1 answer
  • The ANOVA procedure is a statistical approach for determining whether or not the means of:______.
    10·1 answer
  • Which of the following expressions are equivalent
    10·1 answer
  • A basket of fruit holds 12 apples, 24 pears, and 16 oranges. Find the ratio of apples, pears, and oranges in the basket
    15·2 answers
  • in my fish tank the ratio of the redfish to bluefish is 3:5 there are 20 bluefish how many red fish are there
    11·1 answer
  • How do you completely factor:<br><br> 2x^3 – 5x^2 – 22x + 55
    9·1 answer
  • The measured length is 250 ft. The actual length is 246.9 ft. Find the percent error.
    11·1 answer
  • PLEASE HELP FAST!
    13·1 answer
  • My father is 4 times old as me. after 5 years my father will be 3 times old how old is my father now
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!