How to plot complex plane?

Question

How to find complex numbers plane: $$ |\bar z - i|\geq 2\\ \pi\leq \arg(z+i)\leq 2\pi $$

I got it like that: $$ |\bar z - i| = |z + i| $$ $$ |z + i| \geq 2 $$ $$ \sqrt{a +(b+1)} \geq 2 $$

Answer 1

Welcome to SE!

The circle is $|z+i|\le2$

Now all points with $\pi \le arg(z) \le 2\pi$ are points below the real-axis (Shaded in pink). Thus for $\pi \le arg(z+i) \le 2\pi$ we need to our origin to $(0,-i)$ and plot the same (Shown here in blue).

For $|z+i|\ge2$ you need all points outside the circle and on the circle.