Hi !

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.

iQ

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.