Question

Explain why i^3=-i. What does i^4 equal?

Answer 1

i^4=i^3*i=-i*i=-i^2=-(-1)=1

Answer 2

I dont undertand how though

Answer 3

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

i^4=(i^2)(i^2)=(-1)(-1)=1

Answer 4

you ever tell time by a clock?

Answer 5

yea

Answer 6

this is just clock addition .... but it only has 4 hours around it

Answer 7

i is at 12 oclock; i^2 is at 3oclock; i^3 at 6 oclock; and i^4 at 9 oclock.

does that make sense?

Answer 8

amistre64 u shud try sayin the unit circle...

Answer 9

unit circle is an advanced concept, but yes :)

Answer 10

like this

Answer 11

the reason it changes between is and 1s is that it is actually rotating thru the complex plane;

Answer 12

amistre64 can u give some of u r medals to me? :D lol

Answer 13

sure lol

Answer 14

ya rotation is e^(i\theta)

Answer 15

theres 1 :)

Answer 16

thnx...

Answer 17

if you know how a clock moves from 9 to 3 by adding 6 hours; then this should be easy enough to understand

Answer 18

its also known as modular addition