How would I plot plot $\{z\in\mathbb{C}:|z|^2\ge z +\bar z\}$?
So far I did: \begin{align*} |z|^2 & \ge z +\bar z \\ |a+ib|^2 & \ge a+ib+a-ib \\ a^2 + b^2 & \ge 2a\\ a(a-2)+b^2 & \ge 0 \end{align*}
But I cant seem to get the inequality into a circle or simplify it further so I can see how to plot it.
Also, how do I solve:$ \{z \in \mathbb{C}:Im\left(\frac{z+i}{2i}\right)\le 0\}$? Im not sure how to start this question.