I'm trying to locate my four zeroes of a complex-valued function, in order to apply the Residue Theorem.
After using the quadratic formula, I am left with $$z^2 = [-3 \pm i\sqrt7] / 2$$
writing the left side in exponential form, I get: $$z^2 = 2exp(\pm i\theta)/2$$
which gives $$z=\pm \sqrt2exp(\pm i\theta/2)/2$$
these are my four roots; however, I don't know how to compute $\theta$ explicitly. I tried using that arctan(y/x) formula, and but I'm getting anything that's clean.
Thanks in advance,