You're nearly right. The answer is 4i.
Convert (1-i)(2+2i) to trig notation and then multiply
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?
Hmm, I do not know what you edited, but the answer should be 4i.
You seem to have deduced an angle of 315 degrees for (1+i).
But that angle should be 45 degrees.
It seems you had that before, but then you also got 4, which is still wrong - it really should be 4i.
Note that .