Complex numbers cannot be ordered in the same manner as real numbers. That is, if x and y are both complex numbers then an inequality such as x > y has no meaning.
Real numbers can be ordered. If b - a is positive, then a is less than b; this is written as a < b. Equivalently, b is greater than a is written as b > a. Similarly, a is less than or equal to b is written as a ≤ b; b is greater than or equal to a is written as b ≥ a. Now, the following properties can be deduced:
If a is positive, then a > 0.If a ≠ 0, then a2 > 0.
If a < b, then a + c < b + c.
If a > 0 then a·c < b·c otherwise a·c > b·c.
Either a > 0 or a = 0 or a < 0.
If a < b, and a < c, then a < c.