Toronto Math Forum

MAT334-2018F => MAT334--Lectures & Home Assignments => Topic started by: Min Gyu Woo on September 14, 2018, 11:28:19 AM

Title: First example in class
Post by: Min Gyu Woo 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 $3M^2$ ?
Title: Re: First example in class
Post by: Victor Ivrii on September 14, 2018, 02:30:36 PM
We fixed $z^*$, and $\varepsilon>0$. Then we pick up any $M\ge |z^*|+\varepsilon$. Then $|z^*|\le M$, and $|z|\le |z^*|+|z-z^*|\le M$.