** Please see the attached file for the full problem description **
Please show all work in detail and how all steps.
1. Prove that : ((2)^.5)*|z| ≥ |Re(z)| + Im(z)
2. Suppose that either |z| =1 or |w|=1. Prove that |z-w| = |!-z(bar)*w|
3. Prove that |z|=0 iff z=0
This solution provides a step-by-step explanation for how to prove the given complex variables.