Complex Numbers3

2009-08-14 7:46 am
送10分,好簡單.

Calculate the following expressions
1. i^5
2. i^6
3. i^7
4. i^8
5. 1/i
6. 1/i^2
7. 1/i^3
8. 1.i^4


回答 (3)

2009-08-14 8:48 am
✔ 最佳答案
i = √-1
i^2 = -1
i^3 = i^2.i = -i
i^4 = (i^2)^2 = 1


1.
i^5
= i^4.i
= i ...... (ans)


2.
i^6
= i^4.i^2
= (1)(-1)
= -1 ...... (ans)


3.
i^7
= i^4.i^3
= (1)(-i)
= -i ...... (ans)


4.
i^8
= (i^4)^2
= (1)^2
= 1 ...... (ans)


5.
1/i
= i^4/i
= i^3
= -i ...... (ans)


6.
1/i^2
= i^4/i^2
= i^2
= -1 ...... (ans)


7.
1/i^3
= i^4/i^3
= i ...... (ans)


8.
The question may be 1/i^4 or 1.i^4

1/i^4
= i^4/i^4
= 1 ...... (ans)

1.i^4
= 1(1)
= 1 ...... (ans)
2009-08-14 5:15 pm
More generally, we have, for any integers n:
i^(4n) = 1
i^(4n + 1) = i
i^(4n + 2) = -1
i^(4n + 3) = -i
2009-08-14 7:47 am
i²=-1
i³=-i
i^4=1


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