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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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i^4=i^3*i=-i*i=-i^2=-(-1)=1
I dont undertand how though
i^2=-1 (i^2)(i)=(-1)(i)=-i i^4=(i^2)(i^2)=(-1)(-1)=1

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Other answers:

you ever tell time by a clock?
yea
this is just clock addition .... but it only has 4 hours around it
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?
amistre64 u shud try sayin the unit circle...
unit circle is an advanced concept, but yes :)
like this
1 Attachment
the reason it changes between is and 1s is that it is actually rotating thru the complex plane;
amistre64 can u give some of u r medals to me? :D lol
sure lol
ya rotation is e^(i\theta)
theres 1 :)
thnx...
if you know how a clock moves from 9 to 3 by adding 6 hours; then this should be easy enough to understand
its also known as modular addition

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