## Homework 1

This is where members of the class could exchange ideas about the homework. Here is an example of a math formula that is easy to input:

$ f'(z_0)=\lim_{z\to z_0}\frac{f(z)-f(z_0)}{z-z_0} $

Here's a hint on I.8.3 --Steve Bell

It is straightforward to show that

$ (z,w)\mapsto z+w $

is a continuous mapping

$ (\mathbb C\times \mathbb C)\to\mathbb C $

because

$ |(z+w)-(z_0+w_0)|\le|z-z_0|+|w-w_0| $

and to make this last quantity less than epsilon, it suffices to take

$ |z-z_0|<\epsilon/2 $

and

$ |w-w_0|<\epsilon/2. $

To handle complex multiplication, you will need to use a standard trick:

$ zw-z_0w_0 = zw-zw_0+zw_0-z_0w_0=z(w-w_0)+w_0(z-z_0) $.