What is i^43 equal to?
回答 (7)
2009-09-13 4:42 pm
✔ 最佳答案
i is the square root of -1.When raising i to an integer power, it follows this pattern:
i, -1, -i, 1, i, -1, -i, 1, ...
That pattern repeats every four.
Dividing 43 by 4, we get 10, with a remainder of 3.
That remainder is what we're looking for.
Looking at the pattern, the third number is -i.
So that's your answer: -i
2009-09-13 4:50 pm
It is equal to -i.
Knowing that i = â-1, if you calculate the first powers of i you realise there are only 4 possible results:
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
If you then do i^5 it is the same as i^1, i^6 is the same as i^2 and so on.
To calculate i^n you do n/4, if the result is an integer it means the result is the same as i^4, if its an integer plus 0.25 the result is the same as i^1, if its an integer plus 0.5 the result is i^2 and if it is an integer plus 0.75 the result is i^3.
Doing 43/4 = 10.75 so i^43=i^3=-i.
Knowing that i = â-1, if you calculate the first powers of i you realise there are only 4 possible results:
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
If you then do i^5 it is the same as i^1, i^6 is the same as i^2 and so on.
To calculate i^n you do n/4, if the result is an integer it means the result is the same as i^4, if its an integer plus 0.25 the result is the same as i^1, if its an integer plus 0.5 the result is i^2 and if it is an integer plus 0.75 the result is i^3.
Doing 43/4 = 10.75 so i^43=i^3=-i.
2009-09-13 4:46 pm
Answer is -i.
Because i^4(n)-1 = -i..here n=10..
Gopal
Because i^4(n)-1 = -i..here n=10..
Gopal
2009-09-13 4:45 pm
i^1 = i
i^2= -1
i^3 = i^2 x i = (-1)i = -i
i^4 = i^3 x i = (-i)(i) = -i^2 = -(-1) = 1
i^5 = i^4 x i = 1 (i) = i
i^6 = i^5 x i = i x i = i^2 = -1
We note that the pattern keeps repeating in multiples of 4
43/ 4 = 10 times 4 and the remainder is 3
Therefore, i^43 = i^3 = -i
i^2= -1
i^3 = i^2 x i = (-1)i = -i
i^4 = i^3 x i = (-i)(i) = -i^2 = -(-1) = 1
i^5 = i^4 x i = 1 (i) = i
i^6 = i^5 x i = i x i = i^2 = -1
We note that the pattern keeps repeating in multiples of 4
43/ 4 = 10 times 4 and the remainder is 3
Therefore, i^43 = i^3 = -i
2009-09-13 4:45 pm
( -i )
think of it this way. i = root(-1). therefor i^2 is -1
then, i*i*i= -i
and i*i*i*i=1
i*i*i*i*i=i
therefor i has a pattern making i^43 easier to calculate
every fifth power of i it returns to itself
so u could say i^43 is i^3 which is -i
think of it this way. i = root(-1). therefor i^2 is -1
then, i*i*i= -i
and i*i*i*i=1
i*i*i*i*i=i
therefor i has a pattern making i^43 easier to calculate
every fifth power of i it returns to itself
so u could say i^43 is i^3 which is -i
參考: Math Textbooks
2009-09-13 4:42 pm
i^43
= -i
= -i
2009-09-13 4:40 pm
237
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