Can the boundary of $\{(z_1,z_2) \in \mathbb C^2: \exists z_3 \in \mathbb C,\ |z_1^2 + z_2z_3|<1\}$ be written down explicitly?

Question

Can the boundary of $\{(z_1,z_2) \in \mathbb C^2: \exists z_3 \in \mathbb C,\ |z_1^2 + z_2z_3|<1\}$ be written down explicitly?

Given $(z_1,z_2) \in \mathbb C^2 $, I want to find the distance between this point and the boundary of the given set, but I do not know how to write down the boundary explicitly.