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Math Help - complex question2

  1. #1
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    complex question2

    i am also slightly confused about this.

    complex question2-capture2.jpg
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Using z=e^{it} :

     \displaystyle\int_{\Gamma}z^mz^n\;dz=\ldots=i\disp  laystyle\int_0^{2\pi}e^{(m+n+1)it}\;dt=\ldots
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  3. #3
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    thank you so much.
    from that i get.

    i[(m+n+1)2(pi)ie^((m+n+1)2(pi)i)]

    is that correct?
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  4. #4
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    Quote Originally Posted by shaheen7 View Post
    thank you so much.
    from that i get.

    i[(m+n+1)2(pi)ie^((m+n+1)2(pi)i)]

    is that correct?


    It's hard to understand what you really meant, but it should be

    \displaystyle{i\int\limits^{2\pi}_0e^{(m+n+1)it}\,  dt=\frac{1}{m+n+1}e^{(m+n+1)it}\left|\limits^{2\pi  }_0\right. .

    Now distinguish between m+n\neq -1\mbox{ and }m+n=-1

    Tonio
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  5. #5
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    righttt that is what i was doing i just made a small mistake.

    THANK YOU!
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