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Math Help - Missundestanding of how complex numbers work not helping with fourier analysis

  1. #1
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    Missundestanding of how complex numbers work not helping with fourier analysis

    I am studying electrical engineering at university level in the UK. As part of a course on Circuit and Signal processing I have tutorial sheets on Fourier Analysis.

    I am fine with fourier analysis except when I start to look at exponential fourier series, I have the question, I even have the answers and how the tutor reached the answer (the workings). But I am not understanding how he is jumping from one line to another. I have attached the whole solution but the bit that I am misunderstanding is:

    <br />
r_{m}=\frac{-V}{4\pi^2}\displaystyle\{\frac{-1}{jm}[2\pi]\displaystyle\}

    <br />
\\r_{m}=\frac{-jV}{4m\pi^2}\displaystyle\{[2\pi]\displaystyle\}<br />

    where j = complex number j^2=-1, how is j moving from the denominator to the numerator?

    surely the next line should be

    <br />
\\r_{m}=\frac{V}{j4m\pi^2}\displaystyle\{[2\pi]\displaystyle\}<br />

    Any help would be greatly appreciated. Thanks Ed.
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  2. #2
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    Quote Originally Posted by emmv View Post
    I am studying electrical engineering at university level in the UK. As part of a course on Circuit and Signal processing I have tutorial sheets on Fourier Analysis.

    I am fine with fourier analysis except when I start to look at exponential fourier series, I have the question, I even have the answers and how the tutor reached the answer (the workings). But I am not understanding how he is jumping from one line to another. I have attached the whole solution but the bit that I am misunderstanding is:

    <br />
r_{m}=\frac{-V}{4\pi^2}\displaystyle\{\frac{-1}{jm}[2\pi]\displaystyle\}

    <br />
\\r_{m}=\frac{-jV}{4m\pi^2}\{[2\pi]\}<br />

    where j = complex number j^2=-1, how is j moving from the denominator to the numerator?

    surely the next line should be

    <br />
\\r_{m}=\frac{V}{j4m\pi^2}\displaystyle\{[2\pi]\displaystyle\}<br />

    Any help would be greatly appreciated. Thanks Ed.
    Now multiply top and bottom by j, this gives a j on the top and on the bottom j^2=-1, or just -j on the top:

    <br />
r_{m}=\frac{V}{j4m\pi^2}(2\pi)=\frac{Vj}{j^24m\pi^  2}(2\pi)=\frac{-jV}{4m\pi^2}(2\pi)<br />

    CB
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  3. #3
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    Thanks Captain Black, to clarify my understanding:

    If I had \frac{1}{5} and I multiplied top and bottom by 5 then the answer would be \frac{5}{25} which is still \frac{1}{5} the actual values haven't changed just the figures representing them. So is it the case that with j that j^2 is -1 which effectively gets lost within the other numbers?

    So actually the steps are as below, but then how are you moving the minus from the denominator to the numerator?

    <br />
r_{m}=\frac{V}{j4m\pi^2}(2\pi)=\frac{Vj}{j^24m\pi^  2}(2\pi)=\frac{jV}{(-1)4m\pi^2}(2\pi)<br />

    Thanks, Ed.
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  4. #4
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    Sorry Captain Black, I didn't think before I asked my question. If the fraction was \frac{1}{-5} this would in fact be -\frac{1}{5} as the minus relates to the whole of the fraction. Thank you for helping me with this. Regards Ed.
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