Let $z$ be a complex variable, and write $x = \Re(z)$ and $y = \Im(z)$ for the real and the imaginary parts, respectively. Let $f(z)$ be a complex polynomial. Let $R > 0$ be a real number and $\gamma$ the circle in $\mathbb{C}$ of radius $R$ and centre at 0, oriented in the counterclockwise direction. What is the value of
$$\frac{1}{2\pi \imath R} \int_{\gamma} \left( \Re(f(z))\,\mathrm{d}x + \Im(f(z))\,\mathrm{d}y \right)$$