Hi, im having great difficulity with this integration question.

Explaining your method, compute:

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

Thankyou for any help in advance :)

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- Aug 2nd 2010, 02:07 AMCeMeComplex Integration Question
Hi, im having great difficulity with this integration question.

Explaining your method, compute:

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

Thankyou for any help in advance :) - Aug 2nd 2010, 02:54 AMDefunkt
Recall that you can write

$\displaystyle cos \theta = \frac{1}{2} \cdot ( e^{i \theta} + e^{-i \theta} )$

$\displaystyle sin \theta = \frac{1}{2} \cdot ( e^{i \theta} - e^{-i \theta} )$

Rewrite the integrand using these identities and then substitute $\displaystyle z = e^{i \theta}$ to get an integral over the unit sphere, $\displaystyle \mathbb{S}^1$. From here you can use either Cauchy's theorem or the residue theorem to calculate the integral. - Aug 5th 2010, 12:32 PMCeMeComplex 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

$\displaystyle -2\pi i/\sqrt{11}\\$

Is this correct?

Thankyou for any help in advance - Aug 5th 2010, 12:35 PMAckbeet
Correct answer does not have the negative sign out front. Can you show us more of your work?