(adsbygoogle = window.adsbygoogle || []).push({}); Cauchy Intergral Formula sin(i)??

1. The problem statement, all variables and given/known data

Circle of radius 2 centered at the origin oriented anticlockwise. Evaluate:

[tex]\int\frac{sin(z)}{z^{2} +1}[/tex]

2. Relevant equations

I think I'm supposed to be using the Cauchy Integral Formula, so

[tex]\int\frac{f(z) dz}{z - z_{0}}[/tex] = 2[tex]\pi[/tex]if(z_{0})

3. The attempt at a solution

I rewrote z[tex]^{2}[/tex] +1 = (z +i)(z -i) and took z[tex]_{0}[/tex] =i, (suitable z[tex]_{0}[/tex] within the countour) so f(z) = [tex]\frac{sin(z)}{z + i}[/tex] .

Then 2[tex]\pi[/tex]if( [tex]_{0}[/tex] ) = 2[tex]\pi[/tex]i[tex]\frac{sin(i)}{i + i}[/tex]

But what do I do with sin(i)? Can I takeiin polar form on my real/imaginary axis and say sin(i) = sin([tex]\frac{\pi}{2}[/tex]) = 1 ? Is that correct or have I lost the plot somewhere?

(Sorry, I never seem to get the Latex quite right.)

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# Homework Help: Cauchy Intergral Formula sin(i)?

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