I see now. My point was that you can perfectly write x as x + 2342 i \in \mathbb{Z} without that obeying the equation. So every z that is a solution of the equation, has the property x = \Re{\{z\}} but not every z with the previous property satisfies the equation. The problem was stated in a...
Homework Statement
If a force F = F_0 cos (\omega t) = \Re{\{F_0 e^{i \omega t}\}} is applied to a body of mass m attached to a spring of constant k, and x = \Re\{z\} . Show that the following equation holds:
m \ddot{z} = - k z + Fe^{i \omega t} .
Homework Equations
Newton's second law.
The...