Question

Can someone explain to me the powes of i?

Answer 1

you know whats i ?

Answer 2

variable?

Answer 3

you are in imaginary numbers topic , right ?
so, \(\large i=\sqrt{-1}\)
heard of it ?

Answer 4

Yeah i i heard of it

Answer 5

so, whats i^2 =... ?

Answer 6

1 ?

Answer 7

no!
\(i=\sqrt {-1}\)
squaring both sides,
\(i^2=-1\)
got this ?

Answer 8

ok

Answer 9

to get i^3, just multiply i on both sides
i^3=-i
ok?

Answer 10

ohh ok soo like i^3(-1) or somthing like that?

Answer 11

what ?
i^3 = -i

Answer 12

sorry its really new for me kinda lost

Answer 13

i = sqrt (-1)

so i^2 = -1

i^3 = i*i^2 = i*-1 =-i

which part did u not get ?

Answer 14

if i wanted to find i^4= i^3*i=i*-1
or i^2*i^2=i^2*-1?

Answer 15

both way works but use that i^3=-i

Answer 16

so, i^4 = i^2*i^2 = -1 *-1 = 1
got this ?

Answer 17

Ohh ok i^5= i^2*i*3= -1*-i=i?

Answer 18

corrct! :)

Answer 19

What if i were to do a number like i^36?

Answer 20

we note the pattern,
like i^4 =1, we will get i^8 also =1
i^12 = 1 , i^16 =1 and so on...
do u notice a pattern ?

Answer 21

Yes soo like i^3=-i and i^9= -1 and every like multypul of 3 will be -i

Answer 22

nopes, that worked for multiples of 4

i^3 = i^7 = i^11 =i^15 =... = -i
means if the exponents are \(\huge 4 \) apart, the value is same

Answer 23

similarly,
i^2=i^6=i^10=...= -1

Answer 24

ok i see was about to say same thing lol

Answer 25

cool, so u now understand ?

Answer 26

yeah im getting it more and more soo i^36= 1

Answer 27

correct! :)
can i ask you one ?
i^22 = ... ?

Answer 28

ok -1

Answer 29

good! :)

Answer 30

want few more ?

Answer 31

i^2=-1 i^6=-1......22^i=-1 sure yeah

Answer 32

wat about i^4000000000000001
:)

Answer 33

lol, i was trying to be bit lineant and ask him i^1001

Answer 34

i^4000000000000001 =... ?
i^1001 =.... ?
its easy once you get that i^4 =1

Answer 35

****
\(\large i^{4n}=1\)

Answer 36

ლ(ﾟдﾟლ)

Answer 37

for any integer n

Answer 38

that looks like one of i's lol :P

Answer 39

just so ik i^5 =i^3*i^2=i?

Answer 40

first kill the i^4 s

Answer 41

i^5 = i^4 * i = i
better ?

Answer 42

ohh haha yes

Answer 43

i=-1 if it didnt have a right

Answer 44

or just i

Answer 45

what ?
i = sqrt -1
i^2=-1

Answer 46

ohh yeah yeah i frgot

Answer 47

what questions were u going to throw at me ?

Answer 48

i^4000000000000001 =... ?
i^1001 =.... ?

Answer 49

lets take i^101 first,
how would u go on solving this ?
you know i^4 =1 , so is i^8, so is i^12 and so on...actually when powers are multiples of 4, we get answer =1
so why not separate a power of 4 from 101 ?
100 divisible by 4 right ? so i^100 = 1
so, i^101 = i^100 *i = 1*i=i
got this ?

Answer 50

ok i see how you got i^100=4 i^101 =?

Answer 51

ohh waut nvm i^101 =1

Answer 52

no....i^100 = 1
because 100 is multiple of 4

Answer 53

ohh yeah my bad i messed up typeing that how did u get i^101?

Answer 54

i^101 is just i^100 times i

Answer 55

ok ok i^4000000000000001 =... i^400000000000000 *1^1 would i do that

Answer 56

i^400000000000000 *i^1
yes!
i^400000000000000 *i^1 = 1*i^1 = i

Answer 57

wasn't that easy ?

Answer 58

yeah kinda

Answer 59

same way i^1001 = .... ?
i promise, this is last :P

Answer 60

ok i^1000=1*i=i

Answer 61

i^1001 = i^1000*i^1 = 1*i =i
correct! good work :)

Answer 62

i hope you are more confident on this topic now :)

Answer 63

yes school lesson is really stupid

Answer 64

Thanks

Answer 65

welcome ^_^