I agree with arg(z) and arg(w). However, I don't agree with your arg(zw). How do arguments behave under multiplication?
The question:
Let and w = (1 + i). Find Arg(z) and Arg(w) and hence Arg(zw). Evaluate zw and hence show that . Find a similar expression for
I found:
Arg(z) =
Arg(w) =
Arg(zw) =
zw =
The last bit of the question is giving me trouble. I tried using de Moivre's theorem as follows:
This gives me the argument I want. But I'm unsure of how to solve this. Changing it to sin/cos form (not sure of the proper name for it) seems to be the way to go, but I'm still stumped:
Any assistance would be great!