Visualizing a set of points in $\mathbb{C}^2$

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As the title says, I want to find a way to visualize the set $S=\{p=(p_1,p_2)\in\mathbb{C}^2 : |p_1|=|p_2|\}$. I thought of maybe tori? is it a Riemann surface?. How could I find some other description that allows me to answer this question?