Reddit reviews Complex Variables and Applications

First of all, i think the function you wrote above got fucked up in the saving. im guessing the denominator is quadratic in z. the integral of a complex function over a closed curve is equal to 2 pi i times the sum of the residues. the residue of f at z0 is zero unless f is singular at z0. in your case, find where the denominator is zero and use partial fractions rewrite the fraction as the sum of two fractions. there is a shortcut to compute the residues of 'first order poles' AKA 'simple poles', which is what you now have. your best bet from here is to consult whatever book you are using. if that one sucks i recommend this

> Is there a book out there that's friendlier to engineers?

Two books I've used that are quite friendly are Vector Calculus by Marsden and Tromba, and Complex Variables and Applications by Churchill and Brown.

These aren't like those math books that read like a math dictionary, they're very good to learn from.