## 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:

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

## Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.