calculating DC value from positive frequency with its DC undefined
Assume you have the signal

$$x(t)=a+b\cos(\omega_0t)\tag{1}$$

with some non-zero real-valued constants $a$ and $b$. Now remove DC and the negative frequencies to obtain

$$x'(t)=\frac{b}{2}e^{j\omega_0t}\tag{2}$$

Can you calculate the value $a$ from $(2)$?