Fourier transform of a sum
would the linearity of a fourier property apply?


Of course, why not?


  How would you compute the power and the phase of the sum?


Computing each term in complex numbers, summing and converting to power/phase representation


  a step by step breakdown would greatly be appreciated


\begin{equation}
\begin{split}
C(t)&amp;=\left(1.42 \exp^{-1.192t}- 12.44 \exp^{-1.192t} +11.02 \right) u(t) \\
 &amp; = 1.42 \exp^{-1.192t} u(t) - 12.44 \exp^{-1.192t} u(t) +11.02 u(t)
\end{split}
\end{equation}

\begin{equation}
\mathcal{F}(C(t)) = 1.42 \mathcal{F}\left( \exp^{-1.192t} u(t)\right) - 12.44 \mathcal{F}\left(\exp^{-1.192t} u(t)\right) + 11.02\mathcal{F}\left( u(t)\right)
\end{equation}

Can you go from here? And why aren't you summing your exponential terms?