Homework Help: Phasors and complex numbers

1. The problem statement, all variables and given/known data

What are the phasors F(t) and G(t) corresponding to the following functions:
f(t) = Acosω₁t and g(t) = Acosω₂t

Draw the phasors on Argand diagram as well as F(t)+G(t) at t = [itex]\pi[/itex]/(2ω₁)
and from the diagram get f(t)+g(t) as a cosine identity in the simplest form.


I tried plotting the F(t) + G(t),, but I couldn't get the angle nor the magnitude of it! any help will be appreciated ;)

 

well, assuming that we write the functions on a complex form, we get F(t) = Ae^(iω1t) and G(t) = Ae^(iω2t). And by the way, it is given that ω1<w2 .. so, at the given t, the first argument is pi/2, the second one is not exact, but it's bigger than pi/2.. so, F(t) + G(t) is sum of two vectors drawn in the argand diagram.. but its argument is really complicated, and I'm not sure of it.

 

I got the argument to be pi*(ω2-ω1/4ω1 ... I could use the cosine rule to get the argument, however, I got a complicated result! I dont know if I'm on the right track!