I've gotten into a problem I haven't really worked with before in my numerics classes.

I have an underdetermined nonlinear system of equations with 3 parameters.

Newtons method, Boydens method etc. all include the inverse of the jacobian, but if the system is underdetermined this is not defined as far as I understand as:

\begin{align}

\begin{cases}

A=\cos(\alpha)e^{i\phi}\\

B=\sin(\alpha)e^{i\chi}

\end{cases}

\end{align}

where $A$ and $B$ are known parameters.

Is there any straightforward way or trick to solve this kind of problems?