Is This True For Complex Numbers?

  • Thread starter aisha
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  • #1
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i^57 is simplified to i ?
 

Answers and Replies

  • #2
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i^2 = -1
i^3 = -i
i^4 = 1
i^5 = i

57 is divisible by 3. So, if I remember my calc class then it would be...

-i

(Don't be mad if I am completely wrong though, its just what I remember)
 
  • #3
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Who is correct lol? i or -i? which one?

Nonok said:
i^2 = -1
i^3 = -i
i^4 = 1
i^5 = i

57 is divisible by 3. So, if I remember my calc class then it would be...

-i

(Don't be mad if I am completely wrong though, its just what I remember)

OH NO!! NOW im not sure well I divided the exponent by 4 and got a remainder of 1 which made me think that the answer is simply i
hmmm can someone tell us who is right?
 
  • #4
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i have to type some stuff to make my message longer
answer is:

i^57=i
 
  • #5
Gokul43201
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Science Advisor
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aisha said:
I divided the exponent by 4 and got a remainder of 1 which made me think that the answer is simply i
hmmm can someone tell us who is right?

This is correct.
[tex]i^{57} = i^{(56+1)} = i^{56}*i = (i^4)^{14}*i = 1^{14}*i = 1*i = i [/tex]
 
Last edited:
  • #6
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Oh, so there has to be a remainder of 1, guess I forgot that.

Sorry.
 
  • #7
584
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Gokul43201 said:
This is correct.
[tex]i^{57} = i^{(56+1)} = i^{56}*i = (i^4)^{14}*i = 1^{14}*i = 1*i = i [/tex]


WOW GOKU ur answer is COMPLEX!! lol
holy made me think! A simple question but a long way of simplifying it. Thanks soooo much yayay I got it right. Thanks everyone else for ur help! :tongue2:
 

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