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Math Help - why does i exp(it)=1

  1. #1
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    why does i exp(it)=1

    why does i exp(it)=1?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: why does i exp(it)=1

    Quote Originally Posted by blueyellow View Post
    why does i exp(it)=1?
    It doesn't.

    Do you mean when does i exp(it) = 1?
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    Re: why does i exp(it)=1

    no I'm just trying to make sense of something someone wrote:

    = |∫(t = 0 to π) (iRe^(it) dt) / (1 + R^4 e^(4it))|
    ≤ ∫(t = 0 to π) R dt / |1 + R^4 e^(4it)|
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    MHF Contributor alexmahone's Avatar
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    Re: why does i exp(it)=1

    Quote Originally Posted by blueyellow View Post
    no I'm just trying to make sense of something someone wrote:

    = |∫(t = 0 to π) (iRe^(it) dt) / (1 + R^4 e^(4it))|
    ≤ ∫(t = 0 to π) R dt / |1 + R^4 e^(4it)|
    That's because |i exp(it)| = 1.
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  5. #5
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    Re: why does i exp(it)=1

    why?
    I tired to figure it out but I can't. I have an exam retake tomorrow and I really can't think why |i exp(it)|=1
    so I'd appreciate it if you help
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    MHF Contributor alexmahone's Avatar
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    Re: why does i exp(it)=1

    Quote Originally Posted by blueyellow View Post
    why?
    I tired to figure it out but I can't. I have an exam retake tomorrow and I really can't think why |i exp(it)|=1
    so I'd appreciate it if you help
    |i exp(it)| = |i||exp (it)| = 1*1 = 1
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  7. #7
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    Re: why does i exp(it)=1

    Quote Originally Posted by alexmahone View Post
    |i exp(it)| = |i||exp (it)| = 1*1 = 1
    Just to elaborate: exp(it) = cos(t) + i sin(t) therefore |exp(it)| = cos^2(t) + sin^2(t) = 1. All of which should be known by the OP.
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