Question

simplify
i^5
show steps / solution

Answer 1

the answer is -1 how can you arrive to the answer

Answer 2

\[i^5=i^{(4+1)}=i^4*i^1=(1)*i=i\]

Answer 3

answer is not -1

Answer 4

im sorry yeah "i" is the answer

Answer 5

Yeah, I was gonna say:

\[i^2 = -1\]\[\implies i^5 = i^2\cdot i^2 \cdot i = (-1)(-1)i = i\]

Answer 6

great guys LOL

Answer 7

\[i=\sqrt{-1} \]
\[i^2=\sqrt{-1}\sqrt{-1}=-1\]
\[i^4=\sqrt{-1}\sqrt{-1}\sqrt{-1}\sqrt{-1}=(-1)(-1)\]
so therefore

\[i^5=i\]

Answer 8

this is what i always do:
say we have \[i^a\]
and a=4*b+r
\[i^a=i^{4*b+r}=i^{4*b}*i^r=(i^4)^b*i^r=1^b*i^r=1*i^r=i^r\]

Answer 9

got it tnx

Answer 10

if r=0 (if the remainder is 0) then answer is 1
if r=1 (if the remainder is 1) then the answer is i
if r=2 (if the remainder is 2) then the answer is -1
if r=3 (if the remainder is 3) then the answer is -i

Answer 11

^i like

Answer 12

number theory is your friend

Answer 13

The answer is 1 =]

Answer 14

i

Answer 15

lol my b

Answer 16

i tried to read number theory very think

Answer 17

thick

Answer 18

very think?

Answer 19

lol

Answer 20

math is a huge subject
i'm pretty sure each of the subjects in math are also huge

Answer 21

we can't no everything

Answer 22

know*

Answer 23

it was just super in depth,

Answer 24

nah its all good i am religious but not narrow minded, ive heard these things as well, and also in physics, the movie what the bleep do we know says things like this as well.
but i agree with you that i have heard this as well from other sources

Answer 25

nah i hear you i dont dislike anyone for having different religious views

Answer 26

:)

Answer 27

alright myini have a good night answering peoples questions cause i STRUGGLED TONIghT

Answer 28

lol bye bnut