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I want to plot a specific branch of the function $f(z) = \sqrt{z(z-1)}$ in the space $(x,y,w)$ where $x = \Re(z)$, $y = \Im(z)$ and $w = \Re(f(z))$. Let $z = r_1 e^{i\theta_1}$ and $z-1 = r_2 e^{i\theta_2}$. We can then rewrite $f(z) = \sqrt{r_1...