(adsbygoogle = window.adsbygoogle || []).push({}); 1. Integrate z^{2}/(z^{4}-1) counterclockwise around x^{2}+ 16y^{2}=4

2. Cauchy's Integral Forumula

3. Solution

I found the points z=1,-1,i,-i where the function is not defined. Using partial fractions to split them up, and integral them separately.

Only points z=1,-1 lies in the contour, so...

[tex]\oint0.25/(z-1) + 0.25/(z+1) + 1/(z^2+1) dz[/tex]

= 0.25(2Pi I + 2Pi I) + 0 = Pi I

Ans is 0. can anyone find my mistake?

1. Integrate sinh2z/z^{4}counterclockwise around the unit circle.

2. Cauchy's Integral Forumula

3. Solution

[tex]\oint sinh2z/z^4 = \oint sinh2z/(z-0)^4[/tex]

= 2*PI*i/3! * (sinh2z)'''

Differentiating sinh2z thrice gives 8cosh2z

Hence, integral at z=0 = (8/3)*PI*i

Ans is (8/3)*PI. Again, can anyone spot my mistake.

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# Homework Help: Complex Integral

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