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Math Help - Complex Integration Question

  1. #1
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    Complex Integration Question

    Hi, im having great difficulity with this integration question.

    Explaining your method, compute:

    I=\int_{0}^{2\pi }\frac{d\theta }{ cos\theta + 3 sin\theta - i}

    Thankyou for any help in advance
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  2. #2
    Super Member
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    Quote Originally Posted by CeMe View Post
    Hi, im having great difficulity with this integration question.

    Explaining your method, compute:

    I=\int_{0}^{2\pi }\frac{d\theta }{ cos\theta + 3 sin\theta - i}

    Thankyou for any help in advance
    Recall that you can write
    cos \theta = \frac{1}{2} \cdot ( e^{i \theta} + e^{-i \theta} )
    sin \theta = \frac{1}{2} \cdot ( e^{i \theta} - e^{-i \theta} )

    Rewrite the integrand using these identities and then substitute z = e^{i \theta} to get an integral over the unit sphere,  \mathbb{S}^1. From here you can use either Cauchy's theorem or the residue theorem to calculate the integral.
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  3. #3
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    Complex integration question using residue theorem? -ve or not?

    Hi, thankyou for the help, i used residue theorem, however im am unsure if the answer is negative or not. i got
    -2\pi i/\sqrt{11}\\
    Is this correct?
    Thankyou for any help in advance
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  4. #4
    A Plied Mathematician
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    Correct answer does not have the negative sign out front. Can you show us more of your work?
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