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.

So,is there a way to make complex number inequallity?

Then, -1>-9 => i<3i,so square root of nagetive number changes inequality sign?

I mean is this correct 3i>i?(for example)

Is there a way to make inequality of imaginery numbers?if there is please show a example.