Convert (1-i)(2+2i) to trig notation and then multiply

I get:

$\displaystyle {\sqrt{2}{(cos315+isin315)}*{\sqrt{8}{(cos45+isin4 5)}}$

$\displaystyle 4{(cos360+isin360)}$

$\displaystyle 4$

$\displaystyle 4({cos42+isin42)$Book answer is:

My first part is wrong, why???

Also I have a general question other than this current problem. Why are the angles always the same in each point?