Draw $\{z\in\mathbb{C}|z\overline{z}<3+2\text{Im}(z)\}$ I want to draw the set $\{z\in\mathbb{C}|z\overline{z}<3+2\text{Im}(z)\}$. However, I don't know what to do about $2\text{Im}(z)$.
If the set would be $\{z\in\mathbb{C}|z\overline{z}<3\}$, it'd be quite easy, since $z\overline z=\vert z\vert^2$, so the set would contain all complex numbers inside the circle around the center with radius $r=\sqrt{3}$. But how to interpret $2\text{Im}(z)$?

Since $\operatorname{Im}z = \frac{1}{2i}(z - \bar z)$ the condition can be rewritten as:
$$
z \bar z \lt 3 - i(z-\bar z) \\
z \bar z + i z - i \bar z + 1 \lt 4 \\
(z - i)(\bar z +i) \lt 4 \\
|z-i|^2 \lt 4
$$
Therefore the set is the interior of the disc of radius $2$ centered at $i$.
