# Math Help - Complex Number Ordering.

1. ## Complex Number Ordering.

I have trouble solving this problem from my real analysis class. It would be wonderful if someone could help me out or give me a hint. Thanks very much in advance.

Suppose z=a+bi, w=c+di. Define z<w if a<c, and also if a=c but b<d. Prove that this turns the set of all complex numbers into an ordered set. Does this ordered set have the least-upper-bound property?

2. Originally Posted by EmmWalfer
Suppose z=a+bi, w=c+di. Define z<w if a<c, and also if a=c but b<d. Prove that this turns the set of all complex numbers into an ordered set. Does this ordered set have the least-upper-bound property?
The operations can be ordered. Note $i^2=-1<0$.