Suppose that $g(t)$ is a lowpass complex signal with magnitude (solid line) and phase (dashed line)
To modulate $g(t)$ into a bandpass equivalent signal $f(t)$ with center frequency $f_c$, we compute the in-phase and quadrature components of $g(t)$ as \begin{align} g_I(t) &= \text{Re}\{g(t)\} \\ g_Q(t) &= \text{Im}\{g(t)\} \end{align} and then compute $$ f(t) = g_I(t)\cos(2\pi f_c t) - g_Q(t) \sin(2\pi f_c t) \tag{1} \label{eq1} $$ To make sense of \eqref{eq1}, I am curious to know what $g_I(t)$ and $g_Q(t)$ would look like in the frequency domain as a function of $G(f)$, the Fourier transform of $g(t)$ shown in the picture above. In other words, what does taking the real part and imaginary part do to what is shown in the picture above?