### Author Topic: First example in class  (Read 1423 times)

#### Min Gyu Woo

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##### First example in class
« on: September 14, 2018, 11:28:19 AM »
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 $3M^2$ ?
« Last Edit: September 14, 2018, 02:28:18 PM by Victor Ivrii »

#### Victor Ivrii

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