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r-ruslan [8.4K]
2 years ago
13

What does i^739 equal? explain how you found your answer.

Mathematics
1 answer:
Sophie [7]2 years ago
4 0
<h3>Answer:   -i</h3>

========================================================

Explanation:

i = sqrt(-1)

Lets list out the first few powers of i

  • i^0 = 1
  • i^1 = i
  • i^2 = -1
  • i^3 = i*i^2 = i*(-1) = -i
  • i^4 = (i^2)^2 = (-1)^2 = 1

By the time we reach the fourth power, we repeat the cycle over again (since i^0 is also equal to 1). The cycle is of length 4, which means we'll divide the exponent over 4 to find the remainder. Ignore the quotient. That remainder will determine if we go for i^0, i^1, i^2 or i^3.

For example, i^5 = i^1 because 5/4 leads to a remainder 1.

Another example: i^6 = i^2 since 6/4 = 1 remainder 2

Again, we only care about the remainder to find out which bin we land on.

-------------

Turning to the question your teacher gave you, we have,

739/4 = 184 remainder 3

So i^739 = i^3 = -i

<h3>-i is the final answer</h3>

--------------

Side notes:

  • if i^a = i^b, then a-b is a multiple of 4
  • Recall that the divisibility by 4 trick involves looking at the last two digits of the number. So i^739 is identical to i^39.
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3 0
3 years ago
The display below shows the number of home runs hit by six of the players on the Cardinals baseball team.
Ket [755]

Answer:

8

Step-by-step explanation:

If each baseball= 4 homeruns, and Chester has 5 baseballs next to his name (20 homeruns), then Evan hit 12 home runs because 4*3= 12 and he has 3 baseballs next to his name.

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6 0
3 years ago
Y and x have a proportional relationship, and y = 12 when x = 5. What is the value of y when x = 8?
serious [3.7K]
When x = 8 y = 15

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Hope this helped!
8 0
2 years ago
If -3 is a zero of f(x)= x^3+x^2-21x-45, find all of its zeros and their multiplicities
mr_godi [17]

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Step-by-step explanation:

5 0
3 years ago
What is the product 3x5(2x2+4x+1)
lesya692 [45]

Answer:

6x^7+12x^6+3x^5

Step-by-step explanation:

The given expression is:

3x^5(2x^2+4x+1)

We expand the parenthesis using the distributive property to obtain;

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