How can I represent the $-3 Re(z) - 6 Im(z) \geq -2$ and $Re(z) > 2$ on a complex number plane?

Question

How can I represent the $-3 Re(z) - 6 Im(z) \geq -2$ and $Re(z) > 2$ on a complex number plane?

Is it just $-3 - 6 * i \geq -2$ and $x >2$?

Answer 1

On the complex plane, a plot of $x$ and $y$ is made where the complex number $z$ can is written as $z=x+iy \ \ \ (x,y \in \mathbb{R})$

So $\Re(z)=x$ and $\Im(z)=y$

Thus the inequalities are :

$$-3x-6y \geq -2$$

$$x > 2$$

These regions are easy to interpret in a cartesian system:

Here is a link to the Desmos page of the graph