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## Homework Statement

Show that the solution x(t) = Ge^(iwt), where G is in general complex, can be written in the form x(t) = Dcos(wt - [tex]\delta[/tex]).

D(w) and [tex]\delta[/tex](w) are real functions of w.

## Homework Equations

z = Ae^(i[tex]\phi[/tex])

## The Attempt at a Solution

So I know I should start by writing G in polar form. I am confused though as to how to go to polar form with just the G. Is it simply just Ge^(i[tex]\phi[/tex]). Then, I could use Euler's formula to write:

Ge^(i[tex]\phi[/tex]) = Gcos([tex]\phi[/tex]) + iGsin([tex]\phi[/tex]).

I am not sure where this gets me. Any help on where to go from here or if this is even correct would be much appreciated.