# Phasors and complex numbers

## Homework Statement

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 = $\pi$/(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 ;)

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vela
Staff Emeritus
Homework Helper
Can you describe in detail the Argand diagram you drew?

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.

vela
Staff Emeritus