Let us start with a general description of a signal $x(t)$, which consists of a DC component, with value $A_0$, and a sum of $N$ sinusoidal components, each with a different frequency $f_k$, amplitude $A_k$ and phase $\phi_k$, as
$$ x(t) = A_0 + \sum_{k=1}^{N} A_k\cos \left( 2\pi f_k t+ \phi_k \right). $$
Now by using the Euler equations we can write this equation as the following sum of rotating phasors:
$$ \begin{split} x(t) &= A_0 + \sum_{k=1}^N \bigg\{ \left(\frac{A_k}{2}e^{j\phi_k}\right)e^{j2\pi f_k t} + \left(\frac{A_k}{2}e^{-j\phi_k}\right)e^{-j2\pi f_k t}\bigg\} \newline &= X_0 + \sum_{k=1}^N \bigg\{ \frac{X_k}{2}e^{j2\pi f_k t} + \frac{X_k^*}{2}e^{-j2\pi f_k t} \bigg\}, \end{split} $$
where $X_0 = A_0$ and $X_k = A_ke^{j\phi_k}$. From this description we can derive the following general property: