Cauchy-Riemann Equations

$\displaystyle f(z) = \frac{1}{2} z^2$

$\definecolor{coral}{rgb}{0.9372549019607843, 0.403921568627451, 0.0} \definecolor{turquoise}{rgb}{0.1568627450980392, 0.7450980392156863, 0.7333333333333333} \boldsymbol{ \textcolor{turquoise}{\mathrm{Re} f} } \; | \; \boldsymbol{\textcolor{coral}{\mathrm{Im} f}}$