|z|>2 inequation

Given the inequality:
$$\left|{z}\right| > 2$$
To solve this inequality, we must first solve the corresponding equation:
$$\left|{z}\right| = 2$$
Solve:
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.

1.
$$z \geq 0$$
or
$$0 \leq z \wedge z < \infty$$
we get the equation
$$z - 2 = 0$$
after simplifying we get
$$z - 2 = 0$$
the solution in this interval:
$$z_{1} = 2$$

2.
$$z < 0$$
or
$$-\infty < z \wedge z < 0$$
we get the equation
$$- z - 2 = 0$$
after simplifying we get
$$- z - 2 = 0$$
the solution in this interval:
$$z_{2} = -2$$


$$z_{1} = 2$$
$$z_{2} = -2$$
$$z_{1} = 2$$
$$z_{2} = -2$$
This roots
$$z_{2} = -2$$
$$z_{1} = 2$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$z_{0} < z_{2}$$
For example, let's take the point
$$z_{0} = z_{2} - \frac{1}{10}$$
=
$$-2 + - \frac{1}{10}$$
=
$$- \frac{21}{10}$$
substitute to the expression
$$\left|{z}\right| > 2$$
$$\left|{- \frac{21}{10}}\right| > 2$$

21    
-- > 2
10    

one of the solutions of our inequality is:
$$z < -2$$

 _____           _____          
      \         /
-------ο-------ο-------
       z2      z1

Other solutions will get with the changeover to the next point
etc.
The answer:
$$z < -2$$
$$z > 2$$