How Can Phasors Represent the Function g(t) in Complex Form?

[Dusty912]

sorry I am pretty lost here, do you mind working it out for me?

 

[haruspex]

sorry I am pretty lost here, do you mind working it out for me?

No, I will not do that, and no-one else on this forum should either.
Take the expression you had in post #23 and throw away the imaginary parts. Post what that leaves.
You should have the sum (or difference) of two terms, one with a cos(ωt) in it and the other with a sin(ωt). Call this expression R(t).
Similarly, g(t) has a cos(ωt) term and a sin(ωt) term. We need to arrange that R and g are the same function.
In order that R(t) and g(t) are to be identical functions, the cos term in one must be the same as the cos term in the other. Write that as an equation: (cos term extracted from g(t), complete with its coefficient there) = (cos term from R(t), complete with its coefficient there).