I see... thx~
Too much used to real no... have never thought that there would be a problem on that line
(never thought of posting a question in a forum could get immediate response too~ ^^)
according to my proof, instead of \mid z + \overline{z} \mid \leq 2 \mid z \mid, it is \mid z + \overline{z} \mid \geq 2 \mid z \mid...
z is a complex no. and \overline{z} is its conjugate. Have I mixed up some basic rules in complex no. with those in real no.?
I would like to prove \mid z + \overline{z} \mid \leq 2 \mid z \mid
The first way I could think of:
\begin{multline}
RHS^2 - LHS^2\\
=4\mid z \mid^2 - \mid z + \overline{z} \mid ^ 2\\
=4z\overline{z} - (z + \overline{z})(\overline{z}+z)\\
=4z\overline{z} -...