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Math Help - Proof

  1. #1
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    Proof

    For each k \in \mathbb{Z}, prove:

    i^{4k} = 1, i^{4k+1} = i, i^{4k+2} = -1, i^{4k+3} = -i

    Okay.. so I need help with this. I thought the best way to prove these is by induction? So is induction something like:

    Basis step, let k = 1.

    i^{4*1} = i^{4} = 1 and hence it works

    Now assume its true for i^{4k}. Prove that it's true for i^{4(k+1)}

    i^{4(k+1)} = i^{4k}i^{4}

    We know that i^{4k} is 1, and i^{4} is 1, and hence it's true?

    Something along those lines?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Ideasman View Post
    For each k \in \mathbb{Z}, prove:

    i^{4k} = 1, i^{4k+1} = i, i^{4k+2} = -1, i^{4k+3} = -i

    Okay.. so I need help with this. I thought the best way to prove these is by induction? So is induction something like:

    Basis step, let k = 1.

    i^{4*1} = i^{4} = 1 and hence it works

    Now assume its true for i^{4k}. Prove that it's true for i^{4(k+1)}

    i^{4(k+1)} = i^{4k}i^{4}

    We know that i^{4k} is 1, and i^{4} is 1, and hence it's true?

    Something along those lines?
    yes, that method seems fine to me, though i'd word it differently
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