First example in class

[Min Gyu Woo]

For the example with $z^3 - 3z$

Where did the $M$ come from?

Also what limit were we computing with the function $f(z) = z^3 - 3z$?

Also why is $|z^2 +zz^{*}+z^{*2}|$ less than or equal to $3M^2$ ?

[Victor Ivrii]

We fixed $z^*$, and $\varepsilon>0$. Then we pick up any $M\ge |z^*|+\varepsilon$. Then $|z^*|\le M$, and $|z|\le |z^*|+|z-z^*|\le M$.