Question

If I multiply two complex numbers, do the angles add? (If v1 has an angle of 30 and v2 has an angle of 20, is v1*v2 going to have an angle of 50?)

Answer 1

yes.
cis(x)=cos(x)+i sin(x)=e^(ix)
v1 cis(a) * v2 cis(b) = v1*v2*cis(a)*cis(b)=v1*v2*e^((a+b)i)=v1*v2*cis(a+b)