## Solving underdetermined nonlinear system of 2 equation with 3 unknowns.

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?