## eeblue 3 years ago why is i3 equals to -i??

1. eeblue

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2. eeblue

isnt it?? :'(

3. 03453660

no

4. phi

i^3 = i*i*i what is (i*i) ?

5. 03453660

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6. 03453660

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7. eeblue

omg!! I am so dumb..

8. 03453660

you are learning thats great

9. eeblue

ohh!! I think I am starting to get it.. then could you try solving i120 to let me see?

10. 03453660

is this i^120???

11. phi

I would first figure out what is i^4= i*i*i*i

12. eeblue

what about large numbers to simplify? I cant be doing square rootss of -1 all the time right?

13. eeblue

i^120?? i^99 for example..

14. phi

what is i^4 ?

15. eeblue

1?

16. 03453660

its very easy all you do is you have to remember some formulas i^2 = -1 , i^3 = -1 , and i^4 = 1

17. phi

yes now if you wrote out i^120 it would be (i*i*i*i) * (i*i*i*i) * .... * (i*i*i*i)

18. phi

how many groups of 4 i's are there?

19. 03453660

i^120 = (i^2)^60 = (-1)^60 = 1

20. eeblue

how many groups of 4 i's? 30?

21. phi

and 1 times itself 30 times is still 1

22. 03453660

no dont go for grouping method

23. eeblue

omg!! confused!! :'(( why there's maths on earth!! urgh!!

24. eeblue

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25. eeblue

why plus 0?? *got it from a website*

26. phi

The first step to understanding this is to understand that you have 1*1*1*1*...*1 (30 times) if the problem were i^121 (one more i), it would be 1*1..*1 * i one i left over

27. 03453660

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28. eeblue

okay.. then??

29. phi

once you get the idea, you can use the idea of exponents \[ i^{ab} = (i^a)^{b} \]

30. eeblue

ohh!! okay!! I think I am starting to understand.. omg!!

31. eeblue

03453660, could you try solving i^99?? I would like to see..

32. eeblue

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33. eeblue

lost :((

34. amistre64

what is the remainder when you divide 99 by 4?