Camillo ha scritto:@Zero87
Why do you write that for \( \displaystyle {\left|{z}\right|}={1} \) , it is \( \displaystyle {\left|{g{{\left({z}\right)}}}\right|}={\left|{{z}}^{{7}}-{2}{{z}}^{{5}}-{z}+{1}\right|}={1} \) , while it is \( \displaystyle {\left|{g{{\left({z}\right)}}}\right|}\le{5} \) ?.
Mi sono connesso apposta per correggere l'errore - ah sorry - i take access in this forum because i remember that is an error in my proof.
I wrote:
\( \displaystyle {\left|{g{{\left({z}\right)}}}\right|}={\left|{{z}}^{{7}}-{2}{{z}}^{{5}}-{z}+{1}\right|}={1} \)
That is an example of my personal stupidity and distraction, but the correct (i suppose) soluction is:
\( \displaystyle {\left|{g{{\left({z}\right)}}}\right|}={\left|{{z}}^{{7}}-{2}{{z}}^{{5}}-{z}+{1}\right|}\le{\left|{{z}}^{{7}}\right|}+{\left|-{2}{{z}}^{{5}}\right|}+{\left|-{z}\right|}+{\left|{1}\right|}={5} \) for the triangular inequality. But the result is correct (i controlled also on wolphramalpha.com).
Bye
