Math Is Fun Forum

T33N_T1T4N

Member

Registered: 2007-02-10

Posts: 8

imaginary proof

ok we know
i° =1
i   =i
i² =-1
i³ =-i
and after this it follows a pattern where i^4 equals 1. how could i write a prrof for this

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lets just call it,  i, and get it over with

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,403

Re: imaginary proof

T33N_T1T4N,

i° =1
i   =i
i² =-1
i³ =-i
i^4=i² x i² = (-1)x(-1)=1
Since the product of two negative numbers is a positive number.
As a matter of fact, the cycle continues.
i^(4n+1)=i,
i^(4n+2)=-1,
i^(4n+3)=-i
and i^(4n)=1 where n is a whole number.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: imaginary proof

Just stating it a different way:

And this covers all integers, by the division-remainder theorem.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

T33N_T1T4N

Member

Registered: 2007-02-10

Posts: 8

Re: imaginary proof

ah ok i see. at first i didn't understand where the +1 +2 and  +3 came from...but i see that it if i worked backwords...
i^35     35/4=8+3
so i^35= -i

thanks for helping me with that ganesh and ricky

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lets just call it,  i, and get it over with