Fitting fixed number of complex exponentials to complex signal
Complex A and B are a bit messy. What about using the signal model

$$ f(t) = \sum_{k=1}^{2} A_k\, e^{j(w_k t + \phi_k)} $$

where $w$ is the frequency and $\phi$ is phase.

Since sinusoids are orthogonal, probably the easiest thing to do is to Fourier transform the signal and pick out the two largest peaks in the positive part of the spectrum. These will correspond to the two main sinusoids.