- #1
aisha
- 584
- 0
i^57 is simplified to i ?
Is This True For Complex Numbers?
- Thread starter aisha
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Homework Help Overview
The discussion revolves around the simplification of the expression i^57 in the context of complex numbers, specifically focusing on the powers of the imaginary unit i.
Discussion Character
- Exploratory, Assumption checking, Mixed
Approaches and Questions Raised
- Participants explore different methods of simplifying i^57, including examining the periodicity of powers of i and checking divisibility by 4. Questions arise regarding the correctness of the simplifications leading to either i or -i.
Discussion Status
Multiple interpretations of the simplification process are being explored, with some participants expressing uncertainty about their reasoning. There is a recognition of different approaches, but no explicit consensus has been reached regarding the final answer.
Contextual Notes
Participants reference their previous knowledge from calculus and express uncertainty about the rules governing the powers of i, indicating a need for clarification on the periodicity of these powers.
- #2
Nonok
- 8
- 0
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)
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
aisha
- 584
- 0
Who is correct lol? i or -i? which one?
OH NO! NOW I am 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?
Nonok said:
OH NO! NOW I am 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
vladimir69
- 124
- 0
i have to type some stuff to make my message longer
answer is:
i^57=i
answer is:
i^57=i
- #5
Gokul43201
Staff Emeritus
Science Advisor
Gold Member
- 7,213
- 25
aisha said:
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
Nonok
- 8
- 0
Oh, so there has to be a remainder of 1, guess I forgot that.
Sorry.
Sorry.
- #7
aisha
- 584
- 0
Gokul43201 said:
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!
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