Yes, generally most mathematicians tend to agree that complex numbers cannot be compared by
"greater than" or "less than" relations (at least not in a useful, meaningful manner). But such
a relation can, I believe be defined, though perhaps not in terribly useful manner.
Here's a shot at it. I'll use Q for "theta" since theta isn't on the keyboard.
In re consider r nonnegative and Q in the interval [0degrees,360degrees).
So r is the distance from the origin and Q is the angle involved.
Given two complex numbers z and w we define
1) z is less than w if z is closer to the origin:
2) if z and w are the same distance from the origin then
a) z = w if their angles are the same.
b) z is less than w if z's angle is less than w's angle.
Of course if we let the r be negative and/or the angles to be any positive or negative angle, then
we weave a more tangled web.