<h3>
Answer: -i</h3>
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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.
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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>
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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.
Answer:
i think it is b(-22)
Step-by-step explanation:
i hope this helps
Answer:
the pattern is +2, +6, +10, +14, +18 etc
so its in increment of 4
the rest is trivial
Step-by-step explanation:
Answer:
x = 18 y = 10
Step-by-step explanation:
let the first number be x
let the second number be y
x = y + 8..... equation 1
2x + y = 46.... equation 2
x is the larger number
y is the smaller number.
Rearrange the equation and add equation 1 to equation 2.
x - y = 8
+ 2x + y = 46
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3x + 0 = 54
3x = 54
divide both sides by 3
x = 54/3
x = 18
Substitute x = 18 into equation 1
x = y + 8
18 = y + 8
collect like terms
y = 18-8
y = 10
5(4+y) is the correct answer, you would be adding 4 and y then multiplying the sum by 5
