How to compare two complex numbers?

I am trying to implement Muller's method for computing the complex root of a polynomial.

Here r1,r2 could be complex in nature.

How do i compare r1 and r2. r1 >= r2 doesnt seem to be working. I have read elsewhere that > operator compares only the real part of the complex number. Is this true?

[Matt J]

Yes, it is true. What would you like r1>=r2 to mean?

[Sarath S]

i would like it to return 1 if r1 is geater than or equal to r2.

ex. if r1 = 4 + 3i and r2 = 3 + 5i, then return 0 because |r1| < |r2|.

I thought that > would compare the magnitudes if it deals with complex numbers.

But i do realise that comparing two complex numbers doesnt make much sense.

[Bruno Luong]

Then use

abs(r1) < abs(r2)

You notice this is NOT the same than r1 < r2 even for real numbers.

If you apply the first definition with r1=-4 and r2=2 it returns FALSE, which is kind of not comfortable to believe.

In fact there is no order relation for complex numbers.

TMW decides to implement a order relation on complex field that is extended from real number ordering, but rarely pertinent for application.

[Sarath S]

Okay. Thank you. I'll just go with one of the roots instead of comparing them.