$$\oint_{|z|=1} z^3\cos z~\mathrm dz$$
I tried using $z=r\mathrm e^{i\theta}$, but the integral gets very complicated before evaluating at the bounds. Was this not the right approach?
Also, what should I make of $|z|=1$? I interpreted that as the radius of $z$ being 1 and, because it doesn't specify the angle, all angles between $0$ and $2\pi$, inclusive.
$f(z) = z^3 \cos z$ is holomorphic on $\Bbb C$, and $|z| = 1$ is a closed path. Hence, by using Cauchy's Integral Theorem, $\oint_{|z| = 1} f(z) dz = 0$